A food bank's goal is to collect at least 1,200 pounds of... | SAT Linear inequalities in one or two variables Question, Answer Explained

Question bank / Linear inequalities in one or two variables

Math · AlgebraHard

A food bank's goal is to collect at least $1{,}200$ pounds of food. It has already collected $380$ pounds. Each volunteer is expected to collect between $25$ and $40$ pounds of food. What is the minimum number of volunteers needed to guarantee that the food bank meets its goal?

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Answer: 33

The food bank still needs $1{,}200 - 380 = 820$ pounds. To guarantee the goal, assume each volunteer collects the least possible amount, $25$ pounds. Then $25v \ge 820$ , so $v \ge 32.8$ . The number of volunteers must be a whole number, so at least $33$ volunteers are needed.

Using the greatest amount per volunteer, $40$ pounds, gives $21$ volunteers, which meets the goal only if every volunteer collects the maximum.

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