The bigger bag can cost more and still be the better deal. Check the price of one.
Two bags of peaches have different prices and amounts: 3 peaches for $5, or 4 for $7. Compare the price of one peach in each bag. Here “better buy” means the lower price per peach.
A unit rate is the cost or amount for exactly one. Usually you want dollars per one item. Sometimes you want items per one dollar. Pick one and stick with it. Mixing them is how people buy the expensive bag by accident.
Divide each total by how many you get, then compare. The smaller dollars-per-item is the better buy. The larger items-per-dollar is the better buy too. Same fact, flipped.
The bigger bag can cost more in total and still be cheaper per pound. Always reduce to one. Then the comparison is honest.
Try it. Then open the steps.
Example 1 of 5
Brand A is 3 boxes for $9. Brand B is 5 boxes for $14. Which is the better buy?
| Brand | Boxes | Cost | Cost per box |
|---|---|---|---|
| A | 3 | $9 | 9 ÷ 3 = $3 |
| B | 5 | $14 | 14 ÷ 5 = $2.80 |
Answer: Brand B
Example 2 of 5
On the way home
Pump 1: 8 gallons for $27.20. Pump 2: 5 gallons for $16.50. Which costs less per gallon?
Answer: Pump 2
Example 3 of 5
Produce aisle, dad holding both bags
A 3-pound bag is $5.40. A 5-pound bag is $8.50. Which is the better buy?
| Bag | Pounds | Cost | Cost per pound |
|---|---|---|---|
| 3 lb | 3 | $5.40 | 5.40 ÷ 3 = $1.80 |
| 5 lb | 5 | $8.50 | 8.50 ÷ 5 = $1.70 |
Answer: The 5-pound bag
Example 4 of 5
The counter
A 2-scoop cone is $4.50. A 3-scoop is $6.30. Cheaper dollars per scoop?
Answer: $2.10 per scoop
Example 5 of 5
Outside the stadium
Four tickets for $72, or six tickets for $102. Cheaper dollars per ticket?
Answer: $17 per ticket
Easy to miss: Comparing the totals. $7 is more than $5, so it must be worse. Not if you get more peaches.
Do this: Always reduce to one item or one pound. Then the comparison is honest.
Easy to miss: Rounding too early and flipping the winner.
Do this: Keep the full values while comparing, or use exact fractions. Round the final answer only as the question asks.
22 problems · Camp, Trail, Summit
