16Hit1600
AlgebraHardPrice of one item from two purchases

Algebra practice question

Three apples and two pears cost $2.60, and one apple and four pears cost $2.20. What is the cost, in dollars, of one pear?

Answer: 0.4 or .4 or 0.40

Let a and p be the prices. From the second purchase, a = 2.20 − 4p. Substitute into the first: 3(2.20 − 4p) + 2p = 2.60, so 6.60 − 12p + 2p = 2.60, 10p = 4.00, p = 0.40. (An apple is $0.60.)

Common wrong answers

If you answered 0.6
0.60 is the price of an APPLE; the question asks for a pear.
If you answered 0.55
0.55 is 2.20/4, treating the second purchase as pears only.
If you answered 0.52
0.52 is 2.60/5, treating the first purchase as five identical items.

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