Field Notesgrade 7 math
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Solution key: Which pile is the better deal

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Camp · Which pile is the better deal

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1 of 8 · better-buy-c01

3 for $6 or 5 for $12. What is the cheaper unit price, in dollars?

  1. Compare dollars per item, so both options describe the same-size unit. Totals alone are not a fair comparison.
  2. First option: 6 ÷ 3 = 2 dollars per item.
  1. Second option: 12 ÷ 5 = 2.4 dollars per item.
  2. Choose the smaller price because paying less per unit is cheaper. The cheaper unit price is $2.

Answer: 2 dollars

2 of 8 · better-buy-c02

2 pounds for $8 or 5 pounds for $18. Cheaper dollars per pound?

  1. Compare dollars per pound, so both options describe the same-size unit. Totals alone are not a fair comparison.
  2. First option: 8 ÷ 2 = 4 dollars per pound.
  1. Second option: 18 ÷ 5 = 3.6 dollars per pound.
  2. Choose the smaller price because paying less per unit is cheaper. The cheaper price is $3.60 per pound.

Answer: 3.6 dollars per pound

3 of 8 · better-buy-c03

4 tickets for $36 or 3 tickets for $30. Cheaper dollars per ticket?

  1. Compare dollars per ticket, so both options describe the same-size unit. Totals alone are not a fair comparison.
  2. First option: 36 ÷ 4 = 9 dollars per ticket.
  1. Second option: 30 ÷ 3 = 10 dollars per ticket.
  2. Choose the smaller price because paying less per unit is cheaper. The cheaper price is $9 per ticket.

Answer: 9 dollars per ticket

4 of 8 · better-buy-c04

6 bottles for $9 or 10 bottles for $16. Cheaper dollars per bottle?

  1. Compare dollars per bottle, so both options describe the same-size unit. Totals alone are not a fair comparison.
  2. First option: 9 ÷ 6 = 1.5 dollars per bottle.
  1. Second option: 16 ÷ 10 = 1.6 dollars per bottle.
  2. Choose the smaller price because paying less per unit is cheaper. The cheaper price is $1.50 per bottle.

Answer: 1.5 dollars per bottle

5 of 8 · better-buy-c05

Which is the better buy: 8 for $20 or 5 for $15? Choose A if 8 for $20, B if 5 for $15.

  1. Compare dollars per item, so both options describe the same-size unit. Totals alone are not a fair comparison.
  2. First option: 20 ÷ 8 = 2.5 dollars per item.
  1. Second option: 15 ÷ 5 = 3 dollars per item.
  2. Choose the smaller price because paying less per unit is cheaper. Option A is cheaper. Choose A.

Answer: A

6 of 8 · better-buy-c06

12 ounces for $4.80 or 16 ounces for $7.20. Cheaper dollars per ounce?

  1. Compare dollars per ounce, so both options describe the same-size unit. Totals alone are not a fair comparison.
  2. First option: 4.8 ÷ 12 = 0.4 dollars per ounce.
  1. Second option: 7.2 ÷ 16 = 0.45 dollars per ounce.
  2. Choose the smaller price because paying less per unit is cheaper. The cheaper price is $0.40 per ounce.

Answer: 0.4 dollars per ounce

7 of 8 · better-buy-c07

9 miles on 3 gallons or 14 miles on 4 gallons. Greater miles per gallon?

  1. Compare miles per gallon, so both options describe the same-size unit. Totals alone are not a fair comparison.
  2. First option: 9 ÷ 3 = 3 miles per gallon.
  1. Second option: 14 ÷ 4 = 3.5 miles per gallon.
  2. Choose the larger miles-per-gallon rate because it means traveling farther on the same amount of fuel. The greater rate is 3.5 miles per gallon.

Answer: 3.5 mpg

8 of 8 · better-buy-c08

2 hours to walk 7 miles or 3 hours to walk 12 miles. Faster miles per hour?

  1. Compare miles per hour, so both options describe the same-size unit. Totals alone are not a fair comparison.
  2. First option: 7 ÷ 2 = 3.5 miles per hour.
  1. Second option: 12 ÷ 3 = 4 miles per hour.
  2. Choose the larger miles-per-hour rate because it means covering more distance in one hour. The faster speed is 4 miles per hour.

Answer: 4 mph