A farmer has at most 120 acres to plant with corn and... | SAT Linear inequalities in one or two variables Question, Answer Explained

Question bank / Linear inequalities in one or two variables

Math · AlgebraHard

A farmer has at most $120$ acres to plant with corn and soybeans. Each acre of corn requires $3$ hours of labor, and each acre of soybeans requires $2$ hours of labor. The farmer has at most $300$ hours of labor available. If the farmer plants $50$ acres of soybeans, what is the greatest whole number of acres of corn the farmer can plant?

$66$

$67$

$70$

$100$

Show answer and explanation

Answer: A

Let $c$ be the number of acres of corn. The land limit gives $c + 50 \le 120$ , so $c \le 70$ . The labor limit gives $3c + 2(50) \le 300$ , so $3c \le 200$ and $c \le 66\frac{2}{3}$ . Both limits must hold, so the greatest whole number of acres is $66$ .

Choice C satisfies the land limit, but it would need $3(70) + 100 = 310$ hours of labor, more than the $300$ available.

Why the other choices are wrong

B. This rounds 66 2/3 up. Planting 67 acres of corn would take 3(67) + 100 = 301 hours, more than 300.
C. 70 acres meets the land limit, but it would take 310 hours of labor, more than the 300 available.
D. This divides 300 by 3 and ignores the 100 hours already needed for the soybeans.

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