ExplanationTranslate what you are told into algebra: 2 ≤ x + y ≤ 5 and 0 ≤ 2x + 3y ≤ 40.

By manipulating the inequalities, you find that 2 − y ≤ x ≤ 5 – y and –2x ≤ 3y ≤ 40 − 2x.

Substitute the endpoints of the values of x into the second inequality: –2(2 – y) ≤ 3y ≤ 40 − 2(2 − y) and –2(5 − y) ≤ 3y ≤ 40 − 2(5 − y).

By solving for y, the first range yields –4 ≤ y ≤ 36, and the second yields –10 ≤ y ≤ 30, meaning –10 ≤ y ≤ 36 overall.

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Sandy

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