Question

At a cafe, the Bishop family pays $12 for a salad, a fruit bowl, and two sandwiches. The Cortez family pays $14 for two salads and two sandwiches. The Donovan family pays $14 for a salad and three fruit bowls. What is the price of a fruit bowl at the cafe?
$2
$3
$4
$5

Answer 1

Let S = salad, F = fruit bowl, X = sandwich.

From Cortez: 2S + 2X = 14 → S + X = 7 → X = 7 − S.
From Bishop: S + F + 2X = 12 → S + F + 2(7 − S) = 12 → −S + F = −2 → F = S − 2.
From Donovan: S + 3F = 14 → S + 3(S − 2) = 14 → 4S − 6 = 14 → S = 5.

Thus F = S − 2 = 3.

Answer: $3.