← Find the per-unit-weight rate first · Multiplicative Comparison and Unit Rate

Find the per-unit-weight rate first · 12 practice problems

3.OA.A.33.MD.A.2

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Generated variants — 12

Freshly produced from the archetype’s parameters — problem, figure, and solution derived together.

Variant 1 easy

At the produce stand, Mia's mom buys $4\ \text{lb}$ of cherry tomatoes that cost $\$2$ per $8\ \text{oz}$ . At the butcher, she buys $1\ \text{lb}$ of pork that costs $\$7$ per pound. How much does Mia's mom spend in all on the cherry tomatoes and the pork?

Your answer

Show solution

1 · Understandwhat's really being asked

Mia's mom buys cherry tomatoes priced at $2 for every 8 oz and pork priced at $7 per pound. We find each item's cost from its per-unit price, then add the two costs.

Givens

Cherry tomatoes: she buys 4 lb (= 64 oz), priced at $2 per 8 oz.
Pork: she buys 1 lb, priced at $7 per pound.
1 lb = 16 oz.

Unknowns

The total amount of money spent on the cherry tomatoes and the pork together.

Constraints

Prices are unit rates: $2 per 8 oz of tomatoes; $7 per 1 lb of pork.
Money amounts are in dollars and cents.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems

This is a money/rate problem, so tracking the units ($ per ounce, $ per pound) keeps the setup correct. It splits naturally into two subproblems (tomato cost, pork cost) that are added at the end.

3 · Execute3 carry out the plan

1Cost of the cherry tomatoes

#8 Analyze the Units 3.MD.A.2

4 lb is 64 oz, and the price is $2 for each 8 oz. There are 64 / 8 = 8 portions of 8 oz, so the tomatoes cost 8 groups of $2.

64 \div 8 = 8,\quad 8 \times \$2 = \$16

Converting 4 lb to 64 oz so the weight matches the 8 oz unit of the price is just unit sense a third grader builds with measurement.

2Cost of the pork

#7 Identify Subproblems 3.OA.A.3

1 lb is 1 whole pound. At $7 per pound, the pork costs 1 x $7 = $7.

1 \times \$7 = \$7

Matching the pork weight to its per-pound price is a within-100 multiplication/division word-problem skill.

3Add the two costs

#7 Identify Subproblems 3.OA.A.3

Add the tomato cost and the pork cost to get the total spent.

\$16 + \$7 = \$23

Combining the two subtotals is a single addition of two money amounts.

Answer: $23

4 · Reviewdoes it hold up?

Tomatoes $16 and pork $7 are both sensible store prices, and the total $23 is a reasonable grocery sum for the two items.

Another way: Use repeated addition to confirm each subtotal, then add $16 + $7 to reach $23.

Standardsmin grade 3

3.MD.A.2 Measure and estimate liquid volumes and masses of objects — Converting pounds to ounces (and 8 oz to half a pound) to match the price units.
3.OA.A.3 Solve multiplication and division word problems within 100 — Finding each item's cost from its unit rate and adding the subtotals.

💡Takeaway. Match the weight to the price's unit, find each cost, then add - that's just Grade 3 unit sense!

Variant 2 easy

At the produce stand, Mia's mom buys $2\ \text{lb}$ of cherry tomatoes that cost $\$3$ per $8\ \text{oz}$ . At the butcher, she buys $2\ \text{lb}$ of pork that costs $\$7$ per pound. How much does Mia's mom spend in all on the cherry tomatoes and the pork?

Your answer

Show solution

1 · Understandwhat's really being asked

Mia's mom buys cherry tomatoes priced at $3 for every 8 oz and pork priced at $7 per pound. We find each item's cost from its per-unit price, then add the two costs.

Givens

Cherry tomatoes: she buys 2 lb (= 32 oz), priced at $3 per 8 oz.
Pork: she buys 2 lb, priced at $7 per pound.
1 lb = 16 oz.

Unknowns

The total amount of money spent on the cherry tomatoes and the pork together.

Constraints

Prices are unit rates: $3 per 8 oz of tomatoes; $7 per 1 lb of pork.
Money amounts are in dollars and cents.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems

This is a money/rate problem, so tracking the units ($ per ounce, $ per pound) keeps the setup correct. It splits naturally into two subproblems (tomato cost, pork cost) that are added at the end.

3 · Execute3 carry out the plan

1Cost of the cherry tomatoes

#8 Analyze the Units 3.MD.A.2

2 lb is 32 oz, and the price is $3 for each 8 oz. There are 32 / 8 = 4 portions of 8 oz, so the tomatoes cost 4 groups of $3.

32 \div 8 = 4,\quad 4 \times \$3 = \$12

Converting 2 lb to 32 oz so the weight matches the 8 oz unit of the price is just unit sense a third grader builds with measurement.

2Cost of the pork

#7 Identify Subproblems 3.OA.A.3

2 lb is 2 whole pounds. At $7 per pound, the pork costs 2 x $7 = $14.

2 \times \$7 = \$14

Matching the pork weight to its per-pound price is a within-100 multiplication/division word-problem skill.

3Add the two costs

#7 Identify Subproblems 3.OA.A.3

Add the tomato cost and the pork cost to get the total spent.

\$12 + \$14 = \$26

Combining the two subtotals is a single addition of two money amounts.

Answer: $26

4 · Reviewdoes it hold up?

Tomatoes $12 and pork $14 are both sensible store prices, and the total $26 is a reasonable grocery sum for the two items.

Another way: Use repeated addition to confirm each subtotal, then add $12 + $14 to reach $26.

Standardsmin grade 3

3.MD.A.2 Measure and estimate liquid volumes and masses of objects — Converting pounds to ounces (and 8 oz to half a pound) to match the price units.
3.OA.A.3 Solve multiplication and division word problems within 100 — Finding each item's cost from its unit rate and adding the subtotals.

💡Takeaway. Match the weight to the price's unit, find each cost, then add - that's just Grade 3 unit sense!

Variant 3 easy

At the produce stand, Mia's mom buys $1\ \text{lb}$ of cherry tomatoes that cost $\$7$ per $8\ \text{oz}$ . At the butcher, she buys $1\ \text{lb}$ of pork that costs $\$5$ per pound. How much does Mia's mom spend in all on the cherry tomatoes and the pork?

Your answer

Show solution

1 · Understandwhat's really being asked

Mia's mom buys cherry tomatoes priced at $7 for every 8 oz and pork priced at $5 per pound. We find each item's cost from its per-unit price, then add the two costs.

Givens

Cherry tomatoes: she buys 1 lb (= 16 oz), priced at $7 per 8 oz.
Pork: she buys 1 lb, priced at $5 per pound.
1 lb = 16 oz.

Unknowns

The total amount of money spent on the cherry tomatoes and the pork together.

Constraints

Prices are unit rates: $7 per 8 oz of tomatoes; $5 per 1 lb of pork.
Money amounts are in dollars and cents.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems

This is a money/rate problem, so tracking the units ($ per ounce, $ per pound) keeps the setup correct. It splits naturally into two subproblems (tomato cost, pork cost) that are added at the end.

3 · Execute3 carry out the plan

1Cost of the cherry tomatoes

#8 Analyze the Units 3.MD.A.2

1 lb is 16 oz, and the price is $7 for each 8 oz. There are 16 / 8 = 2 portions of 8 oz, so the tomatoes cost 2 groups of $7.

16 \div 8 = 2,\quad 2 \times \$7 = \$14

Converting 1 lb to 16 oz so the weight matches the 8 oz unit of the price is just unit sense a third grader builds with measurement.

2Cost of the pork

#7 Identify Subproblems 3.OA.A.3

1 lb is 1 whole pound. At $5 per pound, the pork costs 1 x $5 = $5.

1 \times \$5 = \$5

Matching the pork weight to its per-pound price is a within-100 multiplication/division word-problem skill.

3Add the two costs

#7 Identify Subproblems 3.OA.A.3

Add the tomato cost and the pork cost to get the total spent.

\$14 + \$5 = \$19

Combining the two subtotals is a single addition of two money amounts.

Answer: $19

4 · Reviewdoes it hold up?

Tomatoes $14 and pork $5 are both sensible store prices, and the total $19 is a reasonable grocery sum for the two items.

Another way: Use repeated addition to confirm each subtotal, then add $14 + $5 to reach $19.

Standardsmin grade 3

3.MD.A.2 Measure and estimate liquid volumes and masses of objects — Converting pounds to ounces (and 8 oz to half a pound) to match the price units.
3.OA.A.3 Solve multiplication and division word problems within 100 — Finding each item's cost from its unit rate and adding the subtotals.

💡Takeaway. Match the weight to the price's unit, find each cost, then add - that's just Grade 3 unit sense!

Variant 4 easy

At the produce stand, Mia's mom buys $2\ \text{lb}$ of cherry tomatoes that cost $\$5$ per $8\ \text{oz}$ . At the butcher, she buys $2\ \text{lb}$ of pork that costs $\$9$ per pound. How much does Mia's mom spend in all on the cherry tomatoes and the pork?

Your answer

Show solution

1 · Understandwhat's really being asked

Mia's mom buys cherry tomatoes priced at $5 for every 8 oz and pork priced at $9 per pound. We find each item's cost from its per-unit price, then add the two costs.

Givens

Cherry tomatoes: she buys 2 lb (= 32 oz), priced at $5 per 8 oz.
Pork: she buys 2 lb, priced at $9 per pound.
1 lb = 16 oz.

Unknowns

The total amount of money spent on the cherry tomatoes and the pork together.

Constraints

Prices are unit rates: $5 per 8 oz of tomatoes; $9 per 1 lb of pork.
Money amounts are in dollars and cents.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems

This is a money/rate problem, so tracking the units ($ per ounce, $ per pound) keeps the setup correct. It splits naturally into two subproblems (tomato cost, pork cost) that are added at the end.

3 · Execute3 carry out the plan

1Cost of the cherry tomatoes

#8 Analyze the Units 3.MD.A.2

2 lb is 32 oz, and the price is $5 for each 8 oz. There are 32 / 8 = 4 portions of 8 oz, so the tomatoes cost 4 groups of $5.

32 \div 8 = 4,\quad 4 \times \$5 = \$20

Converting 2 lb to 32 oz so the weight matches the 8 oz unit of the price is just unit sense a third grader builds with measurement.

2Cost of the pork

#7 Identify Subproblems 3.OA.A.3

2 lb is 2 whole pounds. At $9 per pound, the pork costs 2 x $9 = $18.

2 \times \$9 = \$18

Matching the pork weight to its per-pound price is a within-100 multiplication/division word-problem skill.

3Add the two costs

#7 Identify Subproblems 3.OA.A.3

Add the tomato cost and the pork cost to get the total spent.

\$20 + \$18 = \$38

Combining the two subtotals is a single addition of two money amounts.

Answer: $38

4 · Reviewdoes it hold up?

Tomatoes $20 and pork $18 are both sensible store prices, and the total $38 is a reasonable grocery sum for the two items.

Another way: Use repeated addition to confirm each subtotal, then add $20 + $18 to reach $38.

Standardsmin grade 3

3.MD.A.2 Measure and estimate liquid volumes and masses of objects — Converting pounds to ounces (and 8 oz to half a pound) to match the price units.
3.OA.A.3 Solve multiplication and division word problems within 100 — Finding each item's cost from its unit rate and adding the subtotals.

💡Takeaway. Match the weight to the price's unit, find each cost, then add - that's just Grade 3 unit sense!

Variant 5 medium

At the produce stand, Mia's mom buys $3\ \text{lb}$ of cherry tomatoes that cost $\$2$ per $8\ \text{oz}$ . At the butcher, she buys $1\ \text{lb}$ of pork that costs $\$10$ per pound. How much does Mia's mom spend in all on the cherry tomatoes and the pork?

Your answer

Show solution

1 · Understandwhat's really being asked

Mia's mom buys cherry tomatoes priced at $2 for every 8 oz and pork priced at $10 per pound. We find each item's cost from its per-unit price, then add the two costs.

Givens

Cherry tomatoes: she buys 3 lb (= 48 oz), priced at $2 per 8 oz.
Pork: she buys 1 lb, priced at $10 per pound.
1 lb = 16 oz.

Unknowns

The total amount of money spent on the cherry tomatoes and the pork together.

Constraints

Prices are unit rates: $2 per 8 oz of tomatoes; $10 per 1 lb of pork.
Money amounts are in dollars and cents.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems

This is a money/rate problem, so tracking the units ($ per ounce, $ per pound) keeps the setup correct. It splits naturally into two subproblems (tomato cost, pork cost) that are added at the end.

3 · Execute3 carry out the plan

1Cost of the cherry tomatoes

#8 Analyze the Units 3.MD.A.2

3 lb is 48 oz, and the price is $2 for each 8 oz. There are 48 / 8 = 6 portions of 8 oz, so the tomatoes cost 6 groups of $2.

48 \div 8 = 6,\quad 6 \times \$2 = \$12

Converting 3 lb to 48 oz so the weight matches the 8 oz unit of the price is just unit sense a third grader builds with measurement.

2Cost of the pork

#7 Identify Subproblems 3.OA.A.3

1 lb is 1 whole pound. At $10 per pound, the pork costs 1 x $10 = $10.

1 \times \$10 = \$10

Matching the pork weight to its per-pound price is a within-100 multiplication/division word-problem skill.

3Add the two costs

#7 Identify Subproblems 3.OA.A.3

Add the tomato cost and the pork cost to get the total spent.

\$12 + \$10 = \$22

Combining the two subtotals is a single addition of two money amounts.

Answer: $22

4 · Reviewdoes it hold up?

Tomatoes $12 and pork $10 are both sensible store prices, and the total $22 is a reasonable grocery sum for the two items.

Another way: Use repeated addition to confirm each subtotal, then add $12 + $10 to reach $22.

Standardsmin grade 3

3.MD.A.2 Measure and estimate liquid volumes and masses of objects — Converting pounds to ounces (and 8 oz to half a pound) to match the price units.
3.OA.A.3 Solve multiplication and division word problems within 100 — Finding each item's cost from its unit rate and adding the subtotals.

💡Takeaway. Match the weight to the price's unit, find each cost, then add - that's just Grade 3 unit sense!

Variant 6 medium

At the produce stand, Mia's mom buys $1\ \text{lb}$ of cherry tomatoes that cost $\$9$ per $8\ \text{oz}$ . At the butcher, she buys $2\ \text{lb}$ of pork that costs $\$12$ per pound. How much does Mia's mom spend in all on the cherry tomatoes and the pork?

Your answer

Show solution

1 · Understandwhat's really being asked

Mia's mom buys cherry tomatoes priced at $9 for every 8 oz and pork priced at $12 per pound. We find each item's cost from its per-unit price, then add the two costs.

Givens

Cherry tomatoes: she buys 1 lb (= 16 oz), priced at $9 per 8 oz.
Pork: she buys 2 lb, priced at $12 per pound.
1 lb = 16 oz.

Unknowns

The total amount of money spent on the cherry tomatoes and the pork together.

Constraints

Prices are unit rates: $9 per 8 oz of tomatoes; $12 per 1 lb of pork.
Money amounts are in dollars and cents.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems

This is a money/rate problem, so tracking the units ($ per ounce, $ per pound) keeps the setup correct. It splits naturally into two subproblems (tomato cost, pork cost) that are added at the end.

3 · Execute3 carry out the plan

1Cost of the cherry tomatoes

#8 Analyze the Units 3.MD.A.2

1 lb is 16 oz, and the price is $9 for each 8 oz. There are 16 / 8 = 2 portions of 8 oz, so the tomatoes cost 2 groups of $9.

16 \div 8 = 2,\quad 2 \times \$9 = \$18

Converting 1 lb to 16 oz so the weight matches the 8 oz unit of the price is just unit sense a third grader builds with measurement.

2Cost of the pork

#7 Identify Subproblems 3.OA.A.3

2 lb is 2 whole pounds. At $12 per pound, the pork costs 2 x $12 = $24.

2 \times \$12 = \$24

Matching the pork weight to its per-pound price is a within-100 multiplication/division word-problem skill.

3Add the two costs

#7 Identify Subproblems 3.OA.A.3

Add the tomato cost and the pork cost to get the total spent.

\$18 + \$24 = \$42

Combining the two subtotals is a single addition of two money amounts.

Answer: $42

4 · Reviewdoes it hold up?

Tomatoes $18 and pork $24 are both sensible store prices, and the total $42 is a reasonable grocery sum for the two items.

Another way: Use repeated addition to confirm each subtotal, then add $18 + $24 to reach $42.

Standardsmin grade 3

3.MD.A.2 Measure and estimate liquid volumes and masses of objects — Converting pounds to ounces (and 8 oz to half a pound) to match the price units.
3.OA.A.3 Solve multiplication and division word problems within 100 — Finding each item's cost from its unit rate and adding the subtotals.

💡Takeaway. Match the weight to the price's unit, find each cost, then add - that's just Grade 3 unit sense!

Variant 7 medium

At the produce stand, Mia's mom buys $2\ \text{lb}$ of cherry tomatoes that cost $\$6$ per $8\ \text{oz}$ . At the butcher, she buys $2\ \text{lb}\ 8\ \text{oz}$ of pork that costs $\$8$ per pound. How much does Mia's mom spend in all on the cherry tomatoes and the pork?

Your answer

Show solution

1 · Understandwhat's really being asked

Mia's mom buys cherry tomatoes priced at $6 for every 8 oz and pork priced at $8 per pound. We find each item's cost from its per-unit price, then add the two costs.

Givens

Cherry tomatoes: she buys 2 lb (= 32 oz), priced at $6 per 8 oz.
Pork: she buys 2 lb 8 oz, priced at $8 per pound.
1 lb = 16 oz.

Unknowns

The total amount of money spent on the cherry tomatoes and the pork together.

Constraints

Prices are unit rates: $6 per 8 oz of tomatoes; $8 per 1 lb of pork.
Money amounts are in dollars and cents.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems

This is a money/rate problem, so tracking the units ($ per ounce, $ per pound) keeps the setup correct. It splits naturally into two subproblems (tomato cost, pork cost) that are added at the end.

3 · Execute3 carry out the plan

1Cost of the cherry tomatoes

#8 Analyze the Units 3.MD.A.2

2 lb is 32 oz, and the price is $6 for each 8 oz. There are 32 / 8 = 4 portions of 8 oz, so the tomatoes cost 4 groups of $6.

32 \div 8 = 4,\quad 4 \times \$6 = \$24

Converting 2 lb to 32 oz so the weight matches the 8 oz unit of the price is just unit sense a third grader builds with measurement.

2Cost of the pork

#7 Identify Subproblems 3.OA.A.3

2 lb 8 oz is 2 whole pounds plus half a pound (8 oz = half of 16 oz). At $8 per pound, 2 pounds cost $16 and the extra half-pound costs half of $8, which is $4.

2\times\$8 + \tfrac{1}{2}\times\$8 = \$16 + \$4 = \$20

Matching the pork weight to its per-pound price is a within-100 multiplication/division word-problem skill.

3Add the two costs

#7 Identify Subproblems 3.OA.A.3

Add the tomato cost and the pork cost to get the total spent.

\$24 + \$20 = \$44

Combining the two subtotals is a single addition of two money amounts.

Answer: $44

4 · Reviewdoes it hold up?

Tomatoes $24 and pork $20 are both sensible store prices, and the total $44 is a reasonable grocery sum for the two items.

Another way: Use repeated addition to confirm each subtotal, then add $24 + $20 to reach $44.

Standardsmin grade 3

3.MD.A.2 Measure and estimate liquid volumes and masses of objects — Converting pounds to ounces (and 8 oz to half a pound) to match the price units.
3.OA.A.3 Solve multiplication and division word problems within 100 — Finding each item's cost from its unit rate and adding the subtotals.

💡Takeaway. Match the weight to the price's unit, find each cost, then add - that's just Grade 3 unit sense!

Variant 8 hard

At the produce stand, Mia's mom buys $3\ \text{lb}$ of cherry tomatoes that cost $\$3$ per $8\ \text{oz}$ . At the butcher, she buys $1\ \text{lb}\ 8\ \text{oz}$ of pork that costs $\$8$ per pound. How much does Mia's mom spend in all on the cherry tomatoes and the pork?

Your answer

Show solution

1 · Understandwhat's really being asked

Mia's mom buys cherry tomatoes priced at $3 for every 8 oz and pork priced at $8 per pound. We find each item's cost from its per-unit price, then add the two costs.

Givens

Cherry tomatoes: she buys 3 lb (= 48 oz), priced at $3 per 8 oz.
Pork: she buys 1 lb 8 oz, priced at $8 per pound.
1 lb = 16 oz.

Unknowns

The total amount of money spent on the cherry tomatoes and the pork together.

Constraints

Prices are unit rates: $3 per 8 oz of tomatoes; $8 per 1 lb of pork.
Money amounts are in dollars and cents.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems

This is a money/rate problem, so tracking the units ($ per ounce, $ per pound) keeps the setup correct. It splits naturally into two subproblems (tomato cost, pork cost) that are added at the end.

3 · Execute3 carry out the plan

1Cost of the cherry tomatoes

#8 Analyze the Units 3.MD.A.2

3 lb is 48 oz, and the price is $3 for each 8 oz. There are 48 / 8 = 6 portions of 8 oz, so the tomatoes cost 6 groups of $3.

48 \div 8 = 6,\quad 6 \times \$3 = \$18

Converting 3 lb to 48 oz so the weight matches the 8 oz unit of the price is just unit sense a third grader builds with measurement.

2Cost of the pork

#7 Identify Subproblems 3.OA.A.3

1 lb 8 oz is 1 whole pound plus half a pound (8 oz = half of 16 oz). At $8 per pound, 1 pound cost $8 and the extra half-pound costs half of $8, which is $4.

1\times\$8 + \tfrac{1}{2}\times\$8 = \$8 + \$4 = \$12

Matching the pork weight to its per-pound price is a within-100 multiplication/division word-problem skill.

3Add the two costs

#7 Identify Subproblems 3.OA.A.3

Add the tomato cost and the pork cost to get the total spent.

\$18 + \$12 = \$30

Combining the two subtotals is a single addition of two money amounts.

Answer: $30

4 · Reviewdoes it hold up?

Tomatoes $18 and pork $12 are both sensible store prices, and the total $30 is a reasonable grocery sum for the two items.

Another way: Use repeated addition to confirm each subtotal, then add $18 + $12 to reach $30.

Standardsmin grade 3

3.MD.A.2 Measure and estimate liquid volumes and masses of objects — Converting pounds to ounces (and 8 oz to half a pound) to match the price units.
3.OA.A.3 Solve multiplication and division word problems within 100 — Finding each item's cost from its unit rate and adding the subtotals.

💡Takeaway. Match the weight to the price's unit, find each cost, then add - that's just Grade 3 unit sense!

Variant 9 hard

At the produce stand, Mia's mom buys $1\ \text{lb}$ of cherry tomatoes that cost $\$8$ per $8\ \text{oz}$ . At the butcher, she buys $4\ \text{lb}\ 8\ \text{oz}$ of pork that costs $\$6$ per pound. How much does Mia's mom spend in all on the cherry tomatoes and the pork?

Your answer

Show solution

1 · Understandwhat's really being asked

Mia's mom buys cherry tomatoes priced at $8 for every 8 oz and pork priced at $6 per pound. We find each item's cost from its per-unit price, then add the two costs.

Givens

Cherry tomatoes: she buys 1 lb (= 16 oz), priced at $8 per 8 oz.
Pork: she buys 4 lb 8 oz, priced at $6 per pound.
1 lb = 16 oz.

Unknowns

The total amount of money spent on the cherry tomatoes and the pork together.

Constraints

Prices are unit rates: $8 per 8 oz of tomatoes; $6 per 1 lb of pork.
Money amounts are in dollars and cents.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems

This is a money/rate problem, so tracking the units ($ per ounce, $ per pound) keeps the setup correct. It splits naturally into two subproblems (tomato cost, pork cost) that are added at the end.

3 · Execute3 carry out the plan

1Cost of the cherry tomatoes

#8 Analyze the Units 3.MD.A.2

1 lb is 16 oz, and the price is $8 for each 8 oz. There are 16 / 8 = 2 portions of 8 oz, so the tomatoes cost 2 groups of $8.

16 \div 8 = 2,\quad 2 \times \$8 = \$16

Converting 1 lb to 16 oz so the weight matches the 8 oz unit of the price is just unit sense a third grader builds with measurement.

2Cost of the pork

#7 Identify Subproblems 3.OA.A.3

4 lb 8 oz is 4 whole pounds plus half a pound (8 oz = half of 16 oz). At $6 per pound, 4 pounds cost $24 and the extra half-pound costs half of $6, which is $3.

4\times\$6 + \tfrac{1}{2}\times\$6 = \$24 + \$3 = \$27

Matching the pork weight to its per-pound price is a within-100 multiplication/division word-problem skill.

3Add the two costs

#7 Identify Subproblems 3.OA.A.3

Add the tomato cost and the pork cost to get the total spent.

\$16 + \$27 = \$43

Combining the two subtotals is a single addition of two money amounts.

Answer: $43

4 · Reviewdoes it hold up?

Tomatoes $16 and pork $27 are both sensible store prices, and the total $43 is a reasonable grocery sum for the two items.

Another way: Use repeated addition to confirm each subtotal, then add $16 + $27 to reach $43.

Standardsmin grade 3

3.MD.A.2 Measure and estimate liquid volumes and masses of objects — Converting pounds to ounces (and 8 oz to half a pound) to match the price units.
3.OA.A.3 Solve multiplication and division word problems within 100 — Finding each item's cost from its unit rate and adding the subtotals.

💡Takeaway. Match the weight to the price's unit, find each cost, then add - that's just Grade 3 unit sense!

Variant 10 hard

At the produce stand, Mia's mom buys $2\ \text{lb}$ of cherry tomatoes that cost $\$4$ per $8\ \text{oz}$ . At the butcher, she buys $3\ \text{lb}\ 8\ \text{oz}$ of pork that costs $\$4$ per pound. How much does Mia's mom spend in all on the cherry tomatoes and the pork?

Your answer

Show solution

1 · Understandwhat's really being asked

Mia's mom buys cherry tomatoes priced at $4 for every 8 oz and pork priced at $4 per pound. We find each item's cost from its per-unit price, then add the two costs.

Givens

Cherry tomatoes: she buys 2 lb (= 32 oz), priced at $4 per 8 oz.
Pork: she buys 3 lb 8 oz, priced at $4 per pound.
1 lb = 16 oz.

Unknowns

The total amount of money spent on the cherry tomatoes and the pork together.

Constraints

Prices are unit rates: $4 per 8 oz of tomatoes; $4 per 1 lb of pork.
Money amounts are in dollars and cents.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems

This is a money/rate problem, so tracking the units ($ per ounce, $ per pound) keeps the setup correct. It splits naturally into two subproblems (tomato cost, pork cost) that are added at the end.

3 · Execute3 carry out the plan

1Cost of the cherry tomatoes

#8 Analyze the Units 3.MD.A.2

2 lb is 32 oz, and the price is $4 for each 8 oz. There are 32 / 8 = 4 portions of 8 oz, so the tomatoes cost 4 groups of $4.

32 \div 8 = 4,\quad 4 \times \$4 = \$16

Converting 2 lb to 32 oz so the weight matches the 8 oz unit of the price is just unit sense a third grader builds with measurement.

2Cost of the pork

#7 Identify Subproblems 3.OA.A.3

3 lb 8 oz is 3 whole pounds plus half a pound (8 oz = half of 16 oz). At $4 per pound, 3 pounds cost $12 and the extra half-pound costs half of $4, which is $2.

3\times\$4 + \tfrac{1}{2}\times\$4 = \$12 + \$2 = \$14

Matching the pork weight to its per-pound price is a within-100 multiplication/division word-problem skill.

3Add the two costs

#7 Identify Subproblems 3.OA.A.3

Add the tomato cost and the pork cost to get the total spent.

\$16 + \$14 = \$30

Combining the two subtotals is a single addition of two money amounts.

Answer: $30

4 · Reviewdoes it hold up?

Tomatoes $16 and pork $14 are both sensible store prices, and the total $30 is a reasonable grocery sum for the two items.

Another way: Use repeated addition to confirm each subtotal, then add $16 + $14 to reach $30.

Standardsmin grade 3

3.MD.A.2 Measure and estimate liquid volumes and masses of objects — Converting pounds to ounces (and 8 oz to half a pound) to match the price units.
3.OA.A.3 Solve multiplication and division word problems within 100 — Finding each item's cost from its unit rate and adding the subtotals.

💡Takeaway. Match the weight to the price's unit, find each cost, then add - that's just Grade 3 unit sense!

Variant 11 medium

At the produce stand, Mia's mom buys $1\ \text{lb}$ of cherry tomatoes that cost $\$5$ per $8\ \text{oz}$ . At the butcher, she buys $3\ \text{lb}\ 8\ \text{oz}$ of pork that costs $\$6$ per pound. How much does Mia's mom spend in all on the cherry tomatoes and the pork?

Your answer

Show solution

1 · Understandwhat's really being asked

Mia's mom buys cherry tomatoes priced at $5 for every 8 oz and pork priced at $6 per pound. We find each item's cost from its per-unit price, then add the two costs.

Givens

Cherry tomatoes: she buys 1 lb (= 16 oz), priced at $5 per 8 oz.
Pork: she buys 3 lb 8 oz, priced at $6 per pound.
1 lb = 16 oz.

Unknowns

The total amount of money spent on the cherry tomatoes and the pork together.

Constraints

Prices are unit rates: $5 per 8 oz of tomatoes; $6 per 1 lb of pork.
Money amounts are in dollars and cents.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems

This is a money/rate problem, so tracking the units ($ per ounce, $ per pound) keeps the setup correct. It splits naturally into two subproblems (tomato cost, pork cost) that are added at the end.

3 · Execute3 carry out the plan

1Cost of the cherry tomatoes

#8 Analyze the Units 3.MD.A.2

1 lb is 16 oz, and the price is $5 for each 8 oz. There are 16 / 8 = 2 portions of 8 oz, so the tomatoes cost 2 groups of $5.

16 \div 8 = 2,\quad 2 \times \$5 = \$10

Converting 1 lb to 16 oz so the weight matches the 8 oz unit of the price is just unit sense a third grader builds with measurement.

2Cost of the pork

#7 Identify Subproblems 3.OA.A.3

3 lb 8 oz is 3 whole pounds plus half a pound (8 oz = half of 16 oz). At $6 per pound, 3 pounds cost $18 and the extra half-pound costs half of $6, which is $3.

3\times\$6 + \tfrac{1}{2}\times\$6 = \$18 + \$3 = \$21

Matching the pork weight to its per-pound price is a within-100 multiplication/division word-problem skill.

3Add the two costs

#7 Identify Subproblems 3.OA.A.3

Add the tomato cost and the pork cost to get the total spent.

\$10 + \$21 = \$31

Combining the two subtotals is a single addition of two money amounts.

Answer: $31

4 · Reviewdoes it hold up?

Tomatoes $10 and pork $21 are both sensible store prices, and the total $31 is a reasonable grocery sum for the two items.

Another way: Use repeated addition to confirm each subtotal, then add $10 + $21 to reach $31.

Standardsmin grade 3

3.MD.A.2 Measure and estimate liquid volumes and masses of objects — Converting pounds to ounces (and 8 oz to half a pound) to match the price units.
3.OA.A.3 Solve multiplication and division word problems within 100 — Finding each item's cost from its unit rate and adding the subtotals.

💡Takeaway. Match the weight to the price's unit, find each cost, then add - that's just Grade 3 unit sense!

Variant 12 hard

At the produce stand, Mia's mom buys $1\ \text{lb}$ of cherry tomatoes that cost $\$4$ per $8\ \text{oz}$ . At the butcher, she buys $1\ \text{lb}\ 8\ \text{oz}$ of pork that costs $\$9$ per pound. How much does Mia's mom spend in all on the cherry tomatoes and the pork?

Your answer

Show solution

1 · Understandwhat's really being asked

Mia's mom buys cherry tomatoes priced at $4 for every 8 oz and pork priced at $9 per pound. We find each item's cost from its per-unit price, then add the two costs.

Givens

Cherry tomatoes: she buys 1 lb (= 16 oz), priced at $4 per 8 oz.
Pork: she buys 1 lb 8 oz, priced at $9 per pound.
1 lb = 16 oz.

Unknowns

The total amount of money spent on the cherry tomatoes and the pork together.

Constraints

Prices are unit rates: $4 per 8 oz of tomatoes; $9 per 1 lb of pork.
Money amounts are in dollars and cents.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems

This is a money/rate problem, so tracking the units ($ per ounce, $ per pound) keeps the setup correct. It splits naturally into two subproblems (tomato cost, pork cost) that are added at the end.

3 · Execute3 carry out the plan

1Cost of the cherry tomatoes

#8 Analyze the Units 3.MD.A.2

1 lb is 16 oz, and the price is $4 for each 8 oz. There are 16 / 8 = 2 portions of 8 oz, so the tomatoes cost 2 groups of $4.

16 \div 8 = 2,\quad 2 \times \$4 = \$8

Converting 1 lb to 16 oz so the weight matches the 8 oz unit of the price is just unit sense a third grader builds with measurement.

2Cost of the pork

#7 Identify Subproblems 3.OA.A.3

1 lb 8 oz is 1 whole pound plus half a pound (8 oz = half of 16 oz). At $9 per pound, 1 pound cost $9 and the extra half-pound costs half of $9, which is $4.50.

1\times\$9 + \tfrac{1}{2}\times\$9 = \$9 + \$4.50 = \$13.50

Matching the pork weight to its per-pound price is a within-100 multiplication/division word-problem skill.

3Add the two costs

#7 Identify Subproblems 3.OA.A.3

Add the tomato cost and the pork cost to get the total spent.

\$8 + \$13.50 = \$21.50

Combining the two subtotals is a single addition of two money amounts.

Answer: $21.50

4 · Reviewdoes it hold up?

Tomatoes $8 and pork $13.50 are both sensible store prices, and the total $21.50 is a reasonable grocery sum for the two items.

Another way: Use repeated addition to confirm each subtotal, then add $8 + $13.50 to reach $21.50.

Standardsmin grade 3

3.MD.A.2 Measure and estimate liquid volumes and masses of objects — Converting pounds to ounces (and 8 oz to half a pound) to match the price units.
3.OA.A.3 Solve multiplication and division word problems within 100 — Finding each item's cost from its unit rate and adding the subtotals.

💡Takeaway. Match the weight to the price's unit, find each cost, then add - that's just Grade 3 unit sense!

Where next?

← Back to the problem: Find the per-unit-weight rate first