Practice · Combine two graphs to find totals · Sensim Math

Variant 1 easy

Mr. Park's class surveyed the number of each snack they bought at the school store and the price of one of each snack. The results are shown in the two bar graphs below. Find how much money the class spent buying bread.

Number of snacks bought (unit: items)

Snack	Crackers	Juice	Bread	Ice cream
Count	$10$	$11$	$13$	$9$

Price of one snack (unit: dollars)

Snack	Crackers	Juice	Bread	Ice cream
Price	$\$1.00$	$\$0.80$	$\$0.90$	$\$1.20$

The data are shown as two bar graphs. The first (horizontal) bar graph shows how many of each snack were bought; the second (vertical) bar graph shows the price of one of each snack in dollars.

Your answer

Show solution

1 · Understandwhat's really being asked

Two bar graphs give, for each snack, how many were bought and the price of one snack. We must find the total money spent on bread by combining bread's count with bread's unit price.

Givens

Counts bought: crackers 10, juice 11, bread 13, ice cream 9.
Prices each: crackers $1.00, juice $0.80, bread $0.90, ice cream $1.20.
We want the money spent on bread only.

Unknowns

The total amount of money the class spent buying bread.

Constraints

Bread count and bread price must come from the same snack.
Total cost = number bought times price of one.

2 · Planchoose the strategy

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

The two graphs supply different units - items and dollars-per-item - and linking the right values multiplies to dollars. Checking units (items times dollars/item = dollars) confirms the setup, and reading the matching bars is the key subproblem.

3 · Execute3 carry out the plan

1Read bread's count

#7 Identify Subproblems 3.MD.B.3

From the 'number of snacks bought' graph, bread was bought 13 times.

\text{bread count} = 13

The bread bar in the count graph reaches 13 items.

2Read bread's unit price

#7 Identify Subproblems 3.MD.B.3

From the 'price of one snack' graph, one bread costs $0.90.

\text{bread price} = \$0.90

The bread bar in the price graph reaches 90 cents per item.

3Check the units and multiply

#8 Analyze the Units 4.OA.A.3

Total money = number of bread times price of one. Units: 13 items times $0.90 per item gives dollars. Compute 13 times $0.90.

13 \times \$0.90 = \$11.70

Multiplying a count by a price-per-item always gives total cost in dollars.

Answer: $11.70

4 · Reviewdoes it hold up?

13 bread at about $0.90 each should be near 13 times $0.90 = $11.70; a quick estimate confirms $11.70 is in the right range and the units are dollars.

Another way: Identify subproblems / repeated addition (tool 7): add the unit price the right number of times, or split the count into friendlier parts and add the partial costs.

Standardsmin grade 4

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading the count and unit price from the two bar graphs.
4.OA.A.3 Solve multi-step word problems using four operations with whole numbers — Multiplying the count by the unit price to get the total money spent.

💡Takeaway. Pull bread's number from one graph and bread's price from the other, then multiply count times price - linking two graphs is just Grade 4 cost = number times price!

Variant 2 easy

Mr. Park's class surveyed the number of each snack they bought at the school store and the price of one of each snack. The results are shown in the two bar graphs below. Find how much money the class spent buying bread.

Number of snacks bought (unit: items)

Snack	Crackers	Juice	Bread	Ice cream
Count	$8$	$12$	$10$	$14$

Price of one snack (unit: dollars)

Snack	Crackers	Juice	Bread	Ice cream
Price	$\$0.90$	$\$0.60$	$\$0.80$	$\$1.10$

The data are shown as two bar graphs. The first (horizontal) bar graph shows how many of each snack were bought; the second (vertical) bar graph shows the price of one of each snack in dollars.

Your answer

Show solution

1 · Understandwhat's really being asked

Two bar graphs give, for each snack, how many were bought and the price of one snack. We must find the total money spent on bread by combining bread's count with bread's unit price.

Givens

Counts bought: crackers 8, juice 12, bread 10, ice cream 14.
Prices each: crackers $0.90, juice $0.60, bread $0.80, ice cream $1.10.
We want the money spent on bread only.

Unknowns

The total amount of money the class spent buying bread.

Constraints

Bread count and bread price must come from the same snack.
Total cost = number bought times price of one.

2 · Planchoose the strategy

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

The two graphs supply different units - items and dollars-per-item - and linking the right values multiplies to dollars. Checking units (items times dollars/item = dollars) confirms the setup, and reading the matching bars is the key subproblem.

3 · Execute3 carry out the plan

1Read bread's count

#7 Identify Subproblems 3.MD.B.3

From the 'number of snacks bought' graph, bread was bought 10 times.

\text{bread count} = 10

The bread bar in the count graph reaches 10 items.

2Read bread's unit price

#7 Identify Subproblems 3.MD.B.3

From the 'price of one snack' graph, one bread costs $0.80.

\text{bread price} = \$0.80

The bread bar in the price graph reaches 80 cents per item.

3Check the units and multiply

#8 Analyze the Units 4.OA.A.3

Total money = number of bread times price of one. Units: 10 items times $0.80 per item gives dollars. Compute 10 times $0.80.

10 \times \$0.80 = \$8.00

Multiplying a count by a price-per-item always gives total cost in dollars.

Answer: $8.00

4 · Reviewdoes it hold up?

10 bread at about $0.80 each should be near 10 times $0.80 = $8.00; a quick estimate confirms $8.00 is in the right range and the units are dollars.

Another way: Identify subproblems / repeated addition (tool 7): add the unit price the right number of times, or split the count into friendlier parts and add the partial costs.

Standardsmin grade 4

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading the count and unit price from the two bar graphs.
4.OA.A.3 Solve multi-step word problems using four operations with whole numbers — Multiplying the count by the unit price to get the total money spent.

💡Takeaway. Pull bread's number from one graph and bread's price from the other, then multiply count times price - linking two graphs is just Grade 4 cost = number times price!

Variant 3 medium

Mr. Park's class surveyed the number of each snack they bought at the school store and the price of one of each snack. The results are shown in the two bar graphs below. Find how much money the class spent buying ice cream.

Number of snacks bought (unit: items)

Snack	Crackers	Juice	Bread	Ice cream
Count	$6$	$9$	$12$	$15$

Price of one snack (unit: dollars)

Snack	Crackers	Juice	Bread	Ice cream
Price	$\$0.80$	$\$0.70$	$\$0.60$	$\$1.00$

The data are shown as two bar graphs. The first (horizontal) bar graph shows how many of each snack were bought; the second (vertical) bar graph shows the price of one of each snack in dollars.

Your answer

Show solution

1 · Understandwhat's really being asked

Two bar graphs give, for each snack, how many were bought and the price of one snack. We must find the total money spent on ice cream by combining ice cream's count with ice cream's unit price.

Givens

Counts bought: crackers 6, juice 9, bread 12, ice cream 15.
Prices each: crackers $0.80, juice $0.70, bread $0.60, ice cream $1.00.
We want the money spent on ice cream only.

Unknowns

The total amount of money the class spent buying ice cream.

Constraints

Ice cream count and ice cream price must come from the same snack.
Total cost = number bought times price of one.

2 · Planchoose the strategy

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

The two graphs supply different units - items and dollars-per-item - and linking the right values multiplies to dollars. Checking units (items times dollars/item = dollars) confirms the setup, and reading the matching bars is the key subproblem.

3 · Execute3 carry out the plan

1Read ice cream's count

#7 Identify Subproblems 3.MD.B.3

From the 'number of snacks bought' graph, ice cream was bought 15 times.

\text{ice cream count} = 15

The ice cream bar in the count graph reaches 15 items.

2Read ice cream's unit price

#7 Identify Subproblems 3.MD.B.3

From the 'price of one snack' graph, one ice cream costs $1.00.

\text{ice cream price} = \$1.00

The ice cream bar in the price graph reaches 100 cents per item.

3Check the units and multiply

#8 Analyze the Units 4.OA.A.3

Total money = number of ice cream times price of one. Units: 15 items times $1.00 per item gives dollars. Compute 15 times $1.00.

15 \times \$1.00 = \$15.00

Multiplying a count by a price-per-item always gives total cost in dollars.

Answer: $15.00

4 · Reviewdoes it hold up?

15 ice cream at about $1.00 each should be near 15 times $1.00 = $15.00; a quick estimate confirms $15.00 is in the right range and the units are dollars.

Another way: Identify subproblems / repeated addition (tool 7): add the unit price the right number of times, or split the count into friendlier parts and add the partial costs.

Standardsmin grade 4

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading the count and unit price from the two bar graphs.
4.OA.A.3 Solve multi-step word problems using four operations with whole numbers — Multiplying the count by the unit price to get the total money spent.

💡Takeaway. Pull ice cream's number from one graph and ice cream's price from the other, then multiply count times price - linking two graphs is just Grade 4 cost = number times price!

Variant 4 medium

Mr. Park's class surveyed the number of each snack they bought at the school store and the price of one of each snack. The results are shown in the two bar graphs below. Find how much money the class spent buying crackers.

Number of snacks bought (unit: items)

Snack	Crackers	Juice	Bread	Ice cream
Count	$15$	$10$	$12$	$8$

Price of one snack (unit: dollars)

Snack	Crackers	Juice	Bread	Ice cream
Price	$\$1.20$	$\$1.00$	$\$0.50$	$\$0.90$

The data are shown as two bar graphs. The first (horizontal) bar graph shows how many of each snack were bought; the second (vertical) bar graph shows the price of one of each snack in dollars.

Your answer

Show solution

1 · Understandwhat's really being asked

Two bar graphs give, for each snack, how many were bought and the price of one snack. We must find the total money spent on crackers by combining crackers's count with crackers's unit price.

Givens

Counts bought: crackers 15, juice 10, bread 12, ice cream 8.
Prices each: crackers $1.20, juice $1.00, bread $0.50, ice cream $0.90.
We want the money spent on crackers only.

Unknowns

The total amount of money the class spent buying crackers.

Constraints

Crackers count and crackers price must come from the same snack.
Total cost = number bought times price of one.

2 · Planchoose the strategy

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

The two graphs supply different units - items and dollars-per-item - and linking the right values multiplies to dollars. Checking units (items times dollars/item = dollars) confirms the setup, and reading the matching bars is the key subproblem.

3 · Execute3 carry out the plan

1Read crackers's count

#7 Identify Subproblems 3.MD.B.3

From the 'number of snacks bought' graph, crackers was bought 15 times.

\text{crackers count} = 15

The crackers bar in the count graph reaches 15 items.

2Read crackers's unit price

#7 Identify Subproblems 3.MD.B.3

From the 'price of one snack' graph, one crackers costs $1.20.

\text{crackers price} = \$1.20

The crackers bar in the price graph reaches 120 cents per item.

3Check the units and multiply

#8 Analyze the Units 4.OA.A.3

Total money = number of crackers times price of one. Units: 15 items times $1.20 per item gives dollars. Compute 15 times $1.20.

15 \times \$1.20 = \$18.00

Multiplying a count by a price-per-item always gives total cost in dollars.

Answer: $18.00

4 · Reviewdoes it hold up?

15 crackers at about $1.20 each should be near 15 times $1.20 = $18.00; a quick estimate confirms $18.00 is in the right range and the units are dollars.

Another way: Identify subproblems / repeated addition (tool 7): add the unit price the right number of times, or split the count into friendlier parts and add the partial costs.

Standardsmin grade 4

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading the count and unit price from the two bar graphs.
4.OA.A.3 Solve multi-step word problems using four operations with whole numbers — Multiplying the count by the unit price to get the total money spent.

💡Takeaway. Pull crackers's number from one graph and crackers's price from the other, then multiply count times price - linking two graphs is just Grade 4 cost = number times price!

Variant 5 medium

Mr. Park's class surveyed the number of each snack they bought at the school store and the price of one of each snack. The results are shown in the two bar graphs below. Find how much money the class spent buying crackers.

Number of snacks bought (unit: items)

Snack	Crackers	Juice	Bread	Ice cream
Count	$12$	$16$	$10$	$14$

Price of one snack (unit: dollars)

Snack	Crackers	Juice	Bread	Ice cream
Price	$\$1.10$	$\$0.75$	$\$0.95$	$\$0.60$

The data are shown as two bar graphs. The first (horizontal) bar graph shows how many of each snack were bought; the second (vertical) bar graph shows the price of one of each snack in dollars.

Your answer

Show solution

1 · Understandwhat's really being asked

Two bar graphs give, for each snack, how many were bought and the price of one snack. We must find the total money spent on crackers by combining crackers's count with crackers's unit price.

Givens

Counts bought: crackers 12, juice 16, bread 10, ice cream 14.
Prices each: crackers $1.10, juice $0.75, bread $0.95, ice cream $0.60.
We want the money spent on crackers only.

Unknowns

The total amount of money the class spent buying crackers.

Constraints

Crackers count and crackers price must come from the same snack.
Total cost = number bought times price of one.

2 · Planchoose the strategy

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

The two graphs supply different units - items and dollars-per-item - and linking the right values multiplies to dollars. Checking units (items times dollars/item = dollars) confirms the setup, and reading the matching bars is the key subproblem.

3 · Execute3 carry out the plan

1Read crackers's count

#7 Identify Subproblems 3.MD.B.3

From the 'number of snacks bought' graph, crackers was bought 12 times.

\text{crackers count} = 12

The crackers bar in the count graph reaches 12 items.

2Read crackers's unit price

#7 Identify Subproblems 3.MD.B.3

From the 'price of one snack' graph, one crackers costs $1.10.

\text{crackers price} = \$1.10

The crackers bar in the price graph reaches 110 cents per item.

3Check the units and multiply

#8 Analyze the Units 4.OA.A.3

Total money = number of crackers times price of one. Units: 12 items times $1.10 per item gives dollars. Compute 12 times $1.10.

12 \times \$1.10 = \$13.20

Multiplying a count by a price-per-item always gives total cost in dollars.

Answer: $13.20

4 · Reviewdoes it hold up?

12 crackers at about $1.10 each should be near 12 times $1.10 = $13.20; a quick estimate confirms $13.20 is in the right range and the units are dollars.

Another way: Identify subproblems / repeated addition (tool 7): add the unit price the right number of times, or split the count into friendlier parts and add the partial costs.

Standardsmin grade 4

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading the count and unit price from the two bar graphs.
4.OA.A.3 Solve multi-step word problems using four operations with whole numbers — Multiplying the count by the unit price to get the total money spent.

💡Takeaway. Pull crackers's number from one graph and crackers's price from the other, then multiply count times price - linking two graphs is just Grade 4 cost = number times price!

Variant 6 hard

Mr. Park's class surveyed the number of each snack they bought at the school store and the price of one of each snack. The results are shown in the two bar graphs below. Find how much money the class spent buying ice cream.

Number of snacks bought (unit: items)

Snack	Crackers	Juice	Bread	Ice cream
Count	$7$	$13$	$16$	$11$

Price of one snack (unit: dollars)

Snack	Crackers	Juice	Bread	Ice cream
Price	$\$0.60$	$\$0.70$	$\$0.80$	$\$1.40$

The data are shown as two bar graphs. The first (horizontal) bar graph shows how many of each snack were bought; the second (vertical) bar graph shows the price of one of each snack in dollars.

Your answer

Show solution

1 · Understandwhat's really being asked

Two bar graphs give, for each snack, how many were bought and the price of one snack. We must find the total money spent on ice cream by combining ice cream's count with ice cream's unit price.

Givens

Counts bought: crackers 7, juice 13, bread 16, ice cream 11.
Prices each: crackers $0.60, juice $0.70, bread $0.80, ice cream $1.40.
We want the money spent on ice cream only.

Unknowns

The total amount of money the class spent buying ice cream.

Constraints

Ice cream count and ice cream price must come from the same snack.
Total cost = number bought times price of one.

2 · Planchoose the strategy

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

The two graphs supply different units - items and dollars-per-item - and linking the right values multiplies to dollars. Checking units (items times dollars/item = dollars) confirms the setup, and reading the matching bars is the key subproblem.

3 · Execute3 carry out the plan

1Read ice cream's count

#7 Identify Subproblems 3.MD.B.3

From the 'number of snacks bought' graph, ice cream was bought 11 times.

\text{ice cream count} = 11

The ice cream bar in the count graph reaches 11 items.

2Read ice cream's unit price

#7 Identify Subproblems 3.MD.B.3

From the 'price of one snack' graph, one ice cream costs $1.40.

\text{ice cream price} = \$1.40

The ice cream bar in the price graph reaches 140 cents per item.

3Check the units and multiply

#8 Analyze the Units 4.OA.A.3

Total money = number of ice cream times price of one. Units: 11 items times $1.40 per item gives dollars. Compute 11 times $1.40.

11 \times \$1.40 = \$15.40

Multiplying a count by a price-per-item always gives total cost in dollars.

Answer: $15.40

4 · Reviewdoes it hold up?

11 ice cream at about $1.40 each should be near 11 times $1.40 = $15.40; a quick estimate confirms $15.40 is in the right range and the units are dollars.

Another way: Identify subproblems / repeated addition (tool 7): add the unit price the right number of times, or split the count into friendlier parts and add the partial costs.

Standardsmin grade 4

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading the count and unit price from the two bar graphs.
4.OA.A.3 Solve multi-step word problems using four operations with whole numbers — Multiplying the count by the unit price to get the total money spent.

💡Takeaway. Pull ice cream's number from one graph and ice cream's price from the other, then multiply count times price - linking two graphs is just Grade 4 cost = number times price!

Variant 7 medium

Mr. Park's class surveyed the number of each snack they bought at the school store and the price of one of each snack. The results are shown in the two bar graphs below. Find how much money the class spent buying bread.

Number of snacks bought (unit: items)

Snack	Crackers	Juice	Bread	Ice cream
Count	$12$	$14$	$16$	$10$

Price of one snack (unit: dollars)

Snack	Crackers	Juice	Bread	Ice cream
Price	$\$1.00$	$\$0.80$	$\$0.70$	$\$1.20$

The data are shown as two bar graphs. The first (horizontal) bar graph shows how many of each snack were bought; the second (vertical) bar graph shows the price of one of each snack in dollars.

Your answer

Show solution

1 · Understandwhat's really being asked

Two bar graphs give, for each snack, how many were bought and the price of one snack. We must find the total money spent on bread by combining bread's count with bread's unit price.

Givens

Counts bought: crackers 12, juice 14, bread 16, ice cream 10.
Prices each: crackers $1.00, juice $0.80, bread $0.70, ice cream $1.20.
We want the money spent on bread only.

Unknowns

The total amount of money the class spent buying bread.

Constraints

Bread count and bread price must come from the same snack.
Total cost = number bought times price of one.

2 · Planchoose the strategy

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

The two graphs supply different units - items and dollars-per-item - and linking the right values multiplies to dollars. Checking units (items times dollars/item = dollars) confirms the setup, and reading the matching bars is the key subproblem.

3 · Execute3 carry out the plan

1Read bread's count

#7 Identify Subproblems 3.MD.B.3

From the 'number of snacks bought' graph, bread was bought 16 times.

\text{bread count} = 16

The bread bar in the count graph reaches 16 items.

2Read bread's unit price

#7 Identify Subproblems 3.MD.B.3

From the 'price of one snack' graph, one bread costs $0.70.

\text{bread price} = \$0.70

The bread bar in the price graph reaches 70 cents per item.

3Check the units and multiply

#8 Analyze the Units 4.OA.A.3

Total money = number of bread times price of one. Units: 16 items times $0.70 per item gives dollars. Compute 16 times $0.70.

16 \times \$0.70 = \$11.20

Multiplying a count by a price-per-item always gives total cost in dollars.

Answer: $11.20

4 · Reviewdoes it hold up?

16 bread at about $0.70 each should be near 16 times $0.70 = $11.20; a quick estimate confirms $11.20 is in the right range and the units are dollars.

Another way: Identify subproblems / repeated addition (tool 7): add the unit price the right number of times, or split the count into friendlier parts and add the partial costs.

Standardsmin grade 4

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading the count and unit price from the two bar graphs.
4.OA.A.3 Solve multi-step word problems using four operations with whole numbers — Multiplying the count by the unit price to get the total money spent.

💡Takeaway. Pull bread's number from one graph and bread's price from the other, then multiply count times price - linking two graphs is just Grade 4 cost = number times price!

Variant 8 hard

Mr. Park's class surveyed the number of each snack they bought at the school store and the price of one of each snack. The results are shown in the two bar graphs below. Find how much money the class spent buying juice.

Number of snacks bought (unit: items)

Snack	Crackers	Juice	Bread	Ice cream
Count	$20$	$14$	$16$	$18$

Price of one snack (unit: dollars)

Snack	Crackers	Juice	Bread	Ice cream
Price	$\$1.50$	$\$0.90$	$\$0.70$	$\$1.30$

The data are shown as two bar graphs. The first (horizontal) bar graph shows how many of each snack were bought; the second (vertical) bar graph shows the price of one of each snack in dollars.

Your answer

Show solution

1 · Understandwhat's really being asked

Two bar graphs give, for each snack, how many were bought and the price of one snack. We must find the total money spent on juice by combining juice's count with juice's unit price.

Givens

Counts bought: crackers 20, juice 14, bread 16, ice cream 18.
Prices each: crackers $1.50, juice $0.90, bread $0.70, ice cream $1.30.
We want the money spent on juice only.

Unknowns

The total amount of money the class spent buying juice.

Constraints

Juice count and juice price must come from the same snack.
Total cost = number bought times price of one.

2 · Planchoose the strategy

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

The two graphs supply different units - items and dollars-per-item - and linking the right values multiplies to dollars. Checking units (items times dollars/item = dollars) confirms the setup, and reading the matching bars is the key subproblem.

3 · Execute3 carry out the plan

1Read juice's count

#7 Identify Subproblems 3.MD.B.3

From the 'number of snacks bought' graph, juice was bought 14 times.

\text{juice count} = 14

The juice bar in the count graph reaches 14 items.

2Read juice's unit price

#7 Identify Subproblems 3.MD.B.3

From the 'price of one snack' graph, one juice costs $0.90.

\text{juice price} = \$0.90

The juice bar in the price graph reaches 90 cents per item.

3Check the units and multiply

#8 Analyze the Units 4.OA.A.3

Total money = number of juice times price of one. Units: 14 items times $0.90 per item gives dollars. Compute 14 times $0.90.

14 \times \$0.90 = \$12.60

Multiplying a count by a price-per-item always gives total cost in dollars.

Answer: $12.60

4 · Reviewdoes it hold up?

14 juice at about $0.90 each should be near 14 times $0.90 = $12.60; a quick estimate confirms $12.60 is in the right range and the units are dollars.

Another way: Identify subproblems / repeated addition (tool 7): add the unit price the right number of times, or split the count into friendlier parts and add the partial costs.

Standardsmin grade 4

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading the count and unit price from the two bar graphs.
4.OA.A.3 Solve multi-step word problems using four operations with whole numbers — Multiplying the count by the unit price to get the total money spent.

💡Takeaway. Pull juice's number from one graph and juice's price from the other, then multiply count times price - linking two graphs is just Grade 4 cost = number times price!

Combine two graphs to find totals · 8 practice problems

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