AlgebraHardPrice per kilogram from two purchases
Algebra practice question
At a market stall, 5 kilograms of apples and 2 kilograms of pears cost $17 in total, and 3 kilograms of apples cost $5 more than 4 kilograms of pears. What is the price, in dollars, of 1 kilogram of apples?
Answer: 3
Let apples cost a and pears p per kilogram: 5a + 2p = 17 and 3a = 4p + 5. From the second, p = (3a − 5)/4; substitute: 5a + (3a − 5)/2 = 17, so 13a − 5 = 34 and a = 3. (Then p = 1.)
Common wrong answers
- If you answered 1
- 1 is the price of pears, not apples.
- If you answered 5
- 5 is the difference in the second purchase, not a price.
- If you answered 17
- 17 is the total for the first purchase, not a price per kilogram.
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