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← 4-1 · Find the value of one unit · Multiplicative Comparison and Unit Rate

Find the value of one unit · 10 practice problems

4.NBT.B.64.OA.A.2

Generated variants — 10

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

Variant 1 answer: The craft store (at $0.25 per marble versus $0.30 at the supermarket).

A craft store sells 5050 marbles for $12.50\$12.50, and a supermarket sells 3232 marbles for $9.60\$9.60. Find which store sells the marbles more cheaply.

Show solution

Understand

A craft store sells 50 marbles for 12.50andasupermarketsells32marblesfor12.50 and a supermarket sells 32 marbles for9.60. Find which store sells marbles more cheaply by comparing the price of a single marble.

Givens
  • Craft store: 50 marbles cost $12.50
  • Supermarket: 32 marbles cost $9.60
  • We want the cheaper store per marble
Unknowns
  • The price of one marble at each store, and which is lower
Constraints
  • Price per marble equals total price divided by the number of marbles
  • The cheaper store is the one with the smaller price per marble

Plan

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

To compare bundles of different sizes fairly, reduce each to the same unit -- the price of one marble (dollars per marble) -- by dividing total price by count. The smaller per-marble price wins.

Execute

#8 Analyze the Units 4.NBT.B.6
Divide the total by the number of marbles: 12.50/50=12.50 / 50 =0.25 per marble.
12.50÷50=0.2512.50 \div 50 = 0.25
Splitting the total cost equally among 50 marbles gives the cost of just one.
#8 Analyze the Units 4.NBT.B.6
Divide the total by the number of marbles: 9.60/32=9.60 / 32 =0.30 per marble.
9.60÷32=0.309.60 \div 32 = 0.30
The same one-unit idea applied to the supermarket bundle.
#7 Identify Subproblems 4.OA.A.2
Compare 0.25and0.25 and0.30 per marble. Since 0.25islessthan0.25 is less than0.30, the craft store sells marbles more cheaply.
0.25<0.300.25 < 0.30
Once both are measured per single marble, the smaller number is the better deal.
Answer: The craft store (at 0.25permarbleversus0.25 per marble versus0.30 at the supermarket).

Review

Cross-check with equal counts: 1600 marbles cost 32 x 12.50=12.50 =400.00 at the craft store but 50 x 9.60=9.60 =480.00 at the supermarket, so the craft store is cheaper, agreeing with the per-marble result.

Identify subproblems (tool 7) by scaling to a common count: find the cost of 1600 marbles at each store and compare 400.00with400.00 with480.00 directly.

Standards · min grade 4

  • 4.OA.A.2 Multiply or divide to solve word problems involving multiplicative comparison — Comparing the two stores by their per-marble unit prices.
  • 4.NBT.B.6 Find whole-number quotients and remainders with up to four-digit dividends — Dividing each total price by the number of marbles to get the unit price.
💡 This only needs Grade 4 dividing -- find the price of one marble at each store, and the smaller one is the better deal!
Variant 2 answer: The supermarket (at $0.35 per marble versus $0.40 at the craft store).

A craft store sells 3535 marbles for $14.00\$14.00, and a supermarket sells 2828 marbles for $9.80\$9.80. Find which store sells the marbles more cheaply.

Show solution

Understand

A craft store sells 35 marbles for 14.00andasupermarketsells28marblesfor14.00 and a supermarket sells 28 marbles for9.80. Find which store sells marbles more cheaply by comparing the price of a single marble.

Givens
  • Craft store: 35 marbles cost $14.00
  • Supermarket: 28 marbles cost $9.80
  • We want the cheaper store per marble
Unknowns
  • The price of one marble at each store, and which is lower
Constraints
  • Price per marble equals total price divided by the number of marbles
  • The cheaper store is the one with the smaller price per marble

Plan

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

To compare bundles of different sizes fairly, reduce each to the same unit -- the price of one marble (dollars per marble) -- by dividing total price by count. The smaller per-marble price wins.

Execute

#8 Analyze the Units 4.NBT.B.6
Divide the total by the number of marbles: 14.00/35=14.00 / 35 =0.40 per marble.
14.00÷35=0.4014.00 \div 35 = 0.40
Splitting the total cost equally among 35 marbles gives the cost of just one.
#8 Analyze the Units 4.NBT.B.6
Divide the total by the number of marbles: 9.80/28=9.80 / 28 =0.35 per marble.
9.80÷28=0.359.80 \div 28 = 0.35
The same one-unit idea applied to the supermarket bundle.
#7 Identify Subproblems 4.OA.A.2
Compare 0.40and0.40 and0.35 per marble. Since 0.35islessthan0.35 is less than0.40, the supermarket sells marbles more cheaply.
0.40>0.350.40 > 0.35
Once both are measured per single marble, the smaller number is the better deal.
Answer: The supermarket (at 0.35permarbleversus0.35 per marble versus0.40 at the craft store).

Review

Cross-check with equal counts: 980 marbles cost 28 x 14.00=14.00 =392.00 at the craft store but 35 x 9.80=9.80 =343.00 at the supermarket, so the supermarket is cheaper, agreeing with the per-marble result.

Identify subproblems (tool 7) by scaling to a common count: find the cost of 980 marbles at each store and compare 392.00with392.00 with343.00 directly.

Standards · min grade 4

  • 4.OA.A.2 Multiply or divide to solve word problems involving multiplicative comparison — Comparing the two stores by their per-marble unit prices.
  • 4.NBT.B.6 Find whole-number quotients and remainders with up to four-digit dividends — Dividing each total price by the number of marbles to get the unit price.
💡 This only needs Grade 4 dividing -- find the price of one marble at each store, and the smaller one is the better deal!
Variant 3 answer: The craft store (at $0.25 per marble versus $0.30 at the supermarket).

A craft store sells 4040 marbles for $10.00\$10.00, and a supermarket sells 2424 marbles for $7.20\$7.20. Find which store sells the marbles more cheaply.

Show solution

Understand

A craft store sells 40 marbles for 10.00andasupermarketsells24marblesfor10.00 and a supermarket sells 24 marbles for7.20. Find which store sells marbles more cheaply by comparing the price of a single marble.

Givens
  • Craft store: 40 marbles cost $10.00
  • Supermarket: 24 marbles cost $7.20
  • We want the cheaper store per marble
Unknowns
  • The price of one marble at each store, and which is lower
Constraints
  • Price per marble equals total price divided by the number of marbles
  • The cheaper store is the one with the smaller price per marble

Plan

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

To compare bundles of different sizes fairly, reduce each to the same unit -- the price of one marble (dollars per marble) -- by dividing total price by count. The smaller per-marble price wins.

Execute

#8 Analyze the Units 4.NBT.B.6
Divide the total by the number of marbles: 10.00/40=10.00 / 40 =0.25 per marble.
10.00÷40=0.2510.00 \div 40 = 0.25
Splitting the total cost equally among 40 marbles gives the cost of just one.
#8 Analyze the Units 4.NBT.B.6
Divide the total by the number of marbles: 7.20/24=7.20 / 24 =0.30 per marble.
7.20÷24=0.307.20 \div 24 = 0.30
The same one-unit idea applied to the supermarket bundle.
#7 Identify Subproblems 4.OA.A.2
Compare 0.25and0.25 and0.30 per marble. Since 0.25islessthan0.25 is less than0.30, the craft store sells marbles more cheaply.
0.25<0.300.25 < 0.30
Once both are measured per single marble, the smaller number is the better deal.
Answer: The craft store (at 0.25permarbleversus0.25 per marble versus0.30 at the supermarket).

Review

Cross-check with equal counts: 960 marbles cost 24 x 10.00=10.00 =240.00 at the craft store but 40 x 7.20=7.20 =288.00 at the supermarket, so the craft store is cheaper, agreeing with the per-marble result.

Identify subproblems (tool 7) by scaling to a common count: find the cost of 960 marbles at each store and compare 240.00with240.00 with288.00 directly.

Standards · min grade 4

  • 4.OA.A.2 Multiply or divide to solve word problems involving multiplicative comparison — Comparing the two stores by their per-marble unit prices.
  • 4.NBT.B.6 Find whole-number quotients and remainders with up to four-digit dividends — Dividing each total price by the number of marbles to get the unit price.
💡 This only needs Grade 4 dividing -- find the price of one marble at each store, and the smaller one is the better deal!
Variant 4 answer: The supermarket (at $0.40 per marble versus $0.45 at the craft store).

A craft store sells 2020 marbles for $9.00\$9.00, and a supermarket sells 1515 marbles for $6.00\$6.00. Find which store sells the marbles more cheaply.

Show solution

Understand

A craft store sells 20 marbles for 9.00andasupermarketsells15marblesfor9.00 and a supermarket sells 15 marbles for6.00. Find which store sells marbles more cheaply by comparing the price of a single marble.

Givens
  • Craft store: 20 marbles cost $9.00
  • Supermarket: 15 marbles cost $6.00
  • We want the cheaper store per marble
Unknowns
  • The price of one marble at each store, and which is lower
Constraints
  • Price per marble equals total price divided by the number of marbles
  • The cheaper store is the one with the smaller price per marble

Plan

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

To compare bundles of different sizes fairly, reduce each to the same unit -- the price of one marble (dollars per marble) -- by dividing total price by count. The smaller per-marble price wins.

Execute

#8 Analyze the Units 4.NBT.B.6
Divide the total by the number of marbles: 9.00/20=9.00 / 20 =0.45 per marble.
9.00÷20=0.459.00 \div 20 = 0.45
Splitting the total cost equally among 20 marbles gives the cost of just one.
#8 Analyze the Units 4.NBT.B.6
Divide the total by the number of marbles: 6.00/15=6.00 / 15 =0.40 per marble.
6.00÷15=0.406.00 \div 15 = 0.40
The same one-unit idea applied to the supermarket bundle.
#7 Identify Subproblems 4.OA.A.2
Compare 0.45and0.45 and0.40 per marble. Since 0.40islessthan0.40 is less than0.45, the supermarket sells marbles more cheaply.
0.45>0.400.45 > 0.40
Once both are measured per single marble, the smaller number is the better deal.
Answer: The supermarket (at 0.40permarbleversus0.40 per marble versus0.45 at the craft store).

Review

Cross-check with equal counts: 300 marbles cost 15 x 9.00=9.00 =135.00 at the craft store but 20 x 6.00=6.00 =120.00 at the supermarket, so the supermarket is cheaper, agreeing with the per-marble result.

Identify subproblems (tool 7) by scaling to a common count: find the cost of 300 marbles at each store and compare 135.00with135.00 with120.00 directly.

Standards · min grade 4

  • 4.OA.A.2 Multiply or divide to solve word problems involving multiplicative comparison — Comparing the two stores by their per-marble unit prices.
  • 4.NBT.B.6 Find whole-number quotients and remainders with up to four-digit dividends — Dividing each total price by the number of marbles to get the unit price.
💡 This only needs Grade 4 dividing -- find the price of one marble at each store, and the smaller one is the better deal!
Variant 5 answer: The craft store (at $0.65 per marble versus $0.75 at the supermarket).

A craft store sells 1515 marbles for $9.75\$9.75, and a supermarket sells 1212 marbles for $9.00\$9.00. Find which store sells the marbles more cheaply.

Show solution

Understand

A craft store sells 15 marbles for 9.75andasupermarketsells12marblesfor9.75 and a supermarket sells 12 marbles for9.00. Find which store sells marbles more cheaply by comparing the price of a single marble.

Givens
  • Craft store: 15 marbles cost $9.75
  • Supermarket: 12 marbles cost $9.00
  • We want the cheaper store per marble
Unknowns
  • The price of one marble at each store, and which is lower
Constraints
  • Price per marble equals total price divided by the number of marbles
  • The cheaper store is the one with the smaller price per marble

Plan

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

To compare bundles of different sizes fairly, reduce each to the same unit -- the price of one marble (dollars per marble) -- by dividing total price by count. The smaller per-marble price wins.

Execute

#8 Analyze the Units 4.NBT.B.6
Divide the total by the number of marbles: 9.75/15=9.75 / 15 =0.65 per marble.
9.75÷15=0.659.75 \div 15 = 0.65
Splitting the total cost equally among 15 marbles gives the cost of just one.
#8 Analyze the Units 4.NBT.B.6
Divide the total by the number of marbles: 9.00/12=9.00 / 12 =0.75 per marble.
9.00÷12=0.759.00 \div 12 = 0.75
The same one-unit idea applied to the supermarket bundle.
#7 Identify Subproblems 4.OA.A.2
Compare 0.65and0.65 and0.75 per marble. Since 0.65islessthan0.65 is less than0.75, the craft store sells marbles more cheaply.
0.65<0.750.65 < 0.75
Once both are measured per single marble, the smaller number is the better deal.
Answer: The craft store (at 0.65permarbleversus0.65 per marble versus0.75 at the supermarket).

Review

Cross-check with equal counts: 180 marbles cost 12 x 9.75=9.75 =117.00 at the craft store but 15 x 9.00=9.00 =135.00 at the supermarket, so the craft store is cheaper, agreeing with the per-marble result.

Identify subproblems (tool 7) by scaling to a common count: find the cost of 180 marbles at each store and compare 117.00with117.00 with135.00 directly.

Standards · min grade 4

  • 4.OA.A.2 Multiply or divide to solve word problems involving multiplicative comparison — Comparing the two stores by their per-marble unit prices.
  • 4.NBT.B.6 Find whole-number quotients and remainders with up to four-digit dividends — Dividing each total price by the number of marbles to get the unit price.
💡 This only needs Grade 4 dividing -- find the price of one marble at each store, and the smaller one is the better deal!
Variant 6 answer: The supermarket (at $0.50 per marble versus $0.60 at the craft store).

A craft store sells 1212 marbles for $7.20\$7.20, and a supermarket sells 3030 marbles for $15.00\$15.00. Find which store sells the marbles more cheaply.

Show solution

Understand

A craft store sells 12 marbles for 7.20andasupermarketsells30marblesfor7.20 and a supermarket sells 30 marbles for15.00. Find which store sells marbles more cheaply by comparing the price of a single marble.

Givens
  • Craft store: 12 marbles cost $7.20
  • Supermarket: 30 marbles cost $15.00
  • We want the cheaper store per marble
Unknowns
  • The price of one marble at each store, and which is lower
Constraints
  • Price per marble equals total price divided by the number of marbles
  • The cheaper store is the one with the smaller price per marble

Plan

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

To compare bundles of different sizes fairly, reduce each to the same unit -- the price of one marble (dollars per marble) -- by dividing total price by count. The smaller per-marble price wins.

Execute

#8 Analyze the Units 4.NBT.B.6
Divide the total by the number of marbles: 7.20/12=7.20 / 12 =0.60 per marble.
7.20÷12=0.607.20 \div 12 = 0.60
Splitting the total cost equally among 12 marbles gives the cost of just one.
#8 Analyze the Units 4.NBT.B.6
Divide the total by the number of marbles: 15.00/30=15.00 / 30 =0.50 per marble.
15.00÷30=0.5015.00 \div 30 = 0.50
The same one-unit idea applied to the supermarket bundle.
#7 Identify Subproblems 4.OA.A.2
Compare 0.60and0.60 and0.50 per marble. Since 0.50islessthan0.50 is less than0.60, the supermarket sells marbles more cheaply.
0.60>0.500.60 > 0.50
Once both are measured per single marble, the smaller number is the better deal.
Answer: The supermarket (at 0.50permarbleversus0.50 per marble versus0.60 at the craft store).

Review

Cross-check with equal counts: 360 marbles cost 30 x 7.20=7.20 =216.00 at the craft store but 12 x 15.00=15.00 =180.00 at the supermarket, so the supermarket is cheaper, agreeing with the per-marble result.

Identify subproblems (tool 7) by scaling to a common count: find the cost of 360 marbles at each store and compare 216.00with216.00 with180.00 directly.

Standards · min grade 4

  • 4.OA.A.2 Multiply or divide to solve word problems involving multiplicative comparison — Comparing the two stores by their per-marble unit prices.
  • 4.NBT.B.6 Find whole-number quotients and remainders with up to four-digit dividends — Dividing each total price by the number of marbles to get the unit price.
💡 This only needs Grade 4 dividing -- find the price of one marble at each store, and the smaller one is the better deal!
Variant 7 answer: The craft store (at $0.20 per marble versus $0.30 at the supermarket).

A craft store sells 2525 marbles for $5.00\$5.00, and a supermarket sells 1818 marbles for $5.40\$5.40. Find which store sells the marbles more cheaply.

Show solution

Understand

A craft store sells 25 marbles for 5.00andasupermarketsells18marblesfor5.00 and a supermarket sells 18 marbles for5.40. Find which store sells marbles more cheaply by comparing the price of a single marble.

Givens
  • Craft store: 25 marbles cost $5.00
  • Supermarket: 18 marbles cost $5.40
  • We want the cheaper store per marble
Unknowns
  • The price of one marble at each store, and which is lower
Constraints
  • Price per marble equals total price divided by the number of marbles
  • The cheaper store is the one with the smaller price per marble

Plan

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

To compare bundles of different sizes fairly, reduce each to the same unit -- the price of one marble (dollars per marble) -- by dividing total price by count. The smaller per-marble price wins.

Execute

#8 Analyze the Units 4.NBT.B.6
Divide the total by the number of marbles: 5.00/25=5.00 / 25 =0.20 per marble.
5.00÷25=0.205.00 \div 25 = 0.20
Splitting the total cost equally among 25 marbles gives the cost of just one.
#8 Analyze the Units 4.NBT.B.6
Divide the total by the number of marbles: 5.40/18=5.40 / 18 =0.30 per marble.
5.40÷18=0.305.40 \div 18 = 0.30
The same one-unit idea applied to the supermarket bundle.
#7 Identify Subproblems 4.OA.A.2
Compare 0.20and0.20 and0.30 per marble. Since 0.20islessthan0.20 is less than0.30, the craft store sells marbles more cheaply.
0.20<0.300.20 < 0.30
Once both are measured per single marble, the smaller number is the better deal.
Answer: The craft store (at 0.20permarbleversus0.20 per marble versus0.30 at the supermarket).

Review

Cross-check with equal counts: 450 marbles cost 18 x 5.00=5.00 =90.00 at the craft store but 25 x 5.40=5.40 =135.00 at the supermarket, so the craft store is cheaper, agreeing with the per-marble result.

Identify subproblems (tool 7) by scaling to a common count: find the cost of 450 marbles at each store and compare 90.00with90.00 with135.00 directly.

Standards · min grade 4

  • 4.OA.A.2 Multiply or divide to solve word problems involving multiplicative comparison — Comparing the two stores by their per-marble unit prices.
  • 4.NBT.B.6 Find whole-number quotients and remainders with up to four-digit dividends — Dividing each total price by the number of marbles to get the unit price.
💡 This only needs Grade 4 dividing -- find the price of one marble at each store, and the smaller one is the better deal!
Variant 8 answer: The craft store (at $0.25 per marble versus $0.30 at the supermarket).

A craft store sells 1616 marbles for $4.00\$4.00, and a supermarket sells 2020 marbles for $6.00\$6.00. Find which store sells the marbles more cheaply.

Show solution

Understand

A craft store sells 16 marbles for 4.00andasupermarketsells20marblesfor4.00 and a supermarket sells 20 marbles for6.00. Find which store sells marbles more cheaply by comparing the price of a single marble.

Givens
  • Craft store: 16 marbles cost $4.00
  • Supermarket: 20 marbles cost $6.00
  • We want the cheaper store per marble
Unknowns
  • The price of one marble at each store, and which is lower
Constraints
  • Price per marble equals total price divided by the number of marbles
  • The cheaper store is the one with the smaller price per marble

Plan

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

To compare bundles of different sizes fairly, reduce each to the same unit -- the price of one marble (dollars per marble) -- by dividing total price by count. The smaller per-marble price wins.

Execute

#8 Analyze the Units 4.NBT.B.6
Divide the total by the number of marbles: 4.00/16=4.00 / 16 =0.25 per marble.
4.00÷16=0.254.00 \div 16 = 0.25
Splitting the total cost equally among 16 marbles gives the cost of just one.
#8 Analyze the Units 4.NBT.B.6
Divide the total by the number of marbles: 6.00/20=6.00 / 20 =0.30 per marble.
6.00÷20=0.306.00 \div 20 = 0.30
The same one-unit idea applied to the supermarket bundle.
#7 Identify Subproblems 4.OA.A.2
Compare 0.25and0.25 and0.30 per marble. Since 0.25islessthan0.25 is less than0.30, the craft store sells marbles more cheaply.
0.25<0.300.25 < 0.30
Once both are measured per single marble, the smaller number is the better deal.
Answer: The craft store (at 0.25permarbleversus0.25 per marble versus0.30 at the supermarket).

Review

Cross-check with equal counts: 320 marbles cost 20 x 4.00=4.00 =80.00 at the craft store but 16 x 6.00=6.00 =96.00 at the supermarket, so the craft store is cheaper, agreeing with the per-marble result.

Identify subproblems (tool 7) by scaling to a common count: find the cost of 320 marbles at each store and compare 80.00with80.00 with96.00 directly.

Standards · min grade 4

  • 4.OA.A.2 Multiply or divide to solve word problems involving multiplicative comparison — Comparing the two stores by their per-marble unit prices.
  • 4.NBT.B.6 Find whole-number quotients and remainders with up to four-digit dividends — Dividing each total price by the number of marbles to get the unit price.
💡 This only needs Grade 4 dividing -- find the price of one marble at each store, and the smaller one is the better deal!
Variant 9 answer: The supermarket (at $0.40 per marble versus $0.45 at the craft store).

A craft store sells 1818 marbles for $8.10\$8.10, and a supermarket sells 2222 marbles for $8.80\$8.80. Find which store sells the marbles more cheaply.

Show solution

Understand

A craft store sells 18 marbles for 8.10andasupermarketsells22marblesfor8.10 and a supermarket sells 22 marbles for8.80. Find which store sells marbles more cheaply by comparing the price of a single marble.

Givens
  • Craft store: 18 marbles cost $8.10
  • Supermarket: 22 marbles cost $8.80
  • We want the cheaper store per marble
Unknowns
  • The price of one marble at each store, and which is lower
Constraints
  • Price per marble equals total price divided by the number of marbles
  • The cheaper store is the one with the smaller price per marble

Plan

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

To compare bundles of different sizes fairly, reduce each to the same unit -- the price of one marble (dollars per marble) -- by dividing total price by count. The smaller per-marble price wins.

Execute

#8 Analyze the Units 4.NBT.B.6
Divide the total by the number of marbles: 8.10/18=8.10 / 18 =0.45 per marble.
8.10÷18=0.458.10 \div 18 = 0.45
Splitting the total cost equally among 18 marbles gives the cost of just one.
#8 Analyze the Units 4.NBT.B.6
Divide the total by the number of marbles: 8.80/22=8.80 / 22 =0.40 per marble.
8.80÷22=0.408.80 \div 22 = 0.40
The same one-unit idea applied to the supermarket bundle.
#7 Identify Subproblems 4.OA.A.2
Compare 0.45and0.45 and0.40 per marble. Since 0.40islessthan0.40 is less than0.45, the supermarket sells marbles more cheaply.
0.45>0.400.45 > 0.40
Once both are measured per single marble, the smaller number is the better deal.
Answer: The supermarket (at 0.40permarbleversus0.40 per marble versus0.45 at the craft store).

Review

Cross-check with equal counts: 396 marbles cost 22 x 8.10=8.10 =178.20 at the craft store but 18 x 8.80=8.80 =158.40 at the supermarket, so the supermarket is cheaper, agreeing with the per-marble result.

Identify subproblems (tool 7) by scaling to a common count: find the cost of 396 marbles at each store and compare 178.20with178.20 with158.40 directly.

Standards · min grade 4

  • 4.OA.A.2 Multiply or divide to solve word problems involving multiplicative comparison — Comparing the two stores by their per-marble unit prices.
  • 4.NBT.B.6 Find whole-number quotients and remainders with up to four-digit dividends — Dividing each total price by the number of marbles to get the unit price.
💡 This only needs Grade 4 dividing -- find the price of one marble at each store, and the smaller one is the better deal!
Variant 10 answer: The supermarket (at $0.30 per marble versus $0.35 at the craft store).

A craft store sells 2424 marbles for $8.40\$8.40, and a supermarket sells 1616 marbles for $4.80\$4.80. Find which store sells the marbles more cheaply.

Show solution

Understand

A craft store sells 24 marbles for 8.40andasupermarketsells16marblesfor8.40 and a supermarket sells 16 marbles for4.80. Find which store sells marbles more cheaply by comparing the price of a single marble.

Givens
  • Craft store: 24 marbles cost $8.40
  • Supermarket: 16 marbles cost $4.80
  • We want the cheaper store per marble
Unknowns
  • The price of one marble at each store, and which is lower
Constraints
  • Price per marble equals total price divided by the number of marbles
  • The cheaper store is the one with the smaller price per marble

Plan

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

To compare bundles of different sizes fairly, reduce each to the same unit -- the price of one marble (dollars per marble) -- by dividing total price by count. The smaller per-marble price wins.

Execute

#8 Analyze the Units 4.NBT.B.6
Divide the total by the number of marbles: 8.40/24=8.40 / 24 =0.35 per marble.
8.40÷24=0.358.40 \div 24 = 0.35
Splitting the total cost equally among 24 marbles gives the cost of just one.
#8 Analyze the Units 4.NBT.B.6
Divide the total by the number of marbles: 4.80/16=4.80 / 16 =0.30 per marble.
4.80÷16=0.304.80 \div 16 = 0.30
The same one-unit idea applied to the supermarket bundle.
#7 Identify Subproblems 4.OA.A.2
Compare 0.35and0.35 and0.30 per marble. Since 0.30islessthan0.30 is less than0.35, the supermarket sells marbles more cheaply.
0.35>0.300.35 > 0.30
Once both are measured per single marble, the smaller number is the better deal.
Answer: The supermarket (at 0.30permarbleversus0.30 per marble versus0.35 at the craft store).

Review

Cross-check with equal counts: 384 marbles cost 16 x 8.40=8.40 =134.40 at the craft store but 24 x 4.80=4.80 =115.20 at the supermarket, so the supermarket is cheaper, agreeing with the per-marble result.

Identify subproblems (tool 7) by scaling to a common count: find the cost of 384 marbles at each store and compare 134.40with134.40 with115.20 directly.

Standards · min grade 4

  • 4.OA.A.2 Multiply or divide to solve word problems involving multiplicative comparison — Comparing the two stores by their per-marble unit prices.
  • 4.NBT.B.6 Find whole-number quotients and remainders with up to four-digit dividends — Dividing each total price by the number of marbles to get the unit price.
💡 This only needs Grade 4 dividing -- find the price of one marble at each store, and the smaller one is the better deal!