SAT Systems of two linear equations in two variables Practice Question 8 (Medium)

Question bank / Systems of two linear equations in two variables

Math · AlgebraMedium

A museum sold $150$ tickets in one day. Adult tickets cost $\$14$ and student tickets cost $\$9$ . The museum collected $\$1{,}750$ from these tickets. How many adult tickets were sold?

$70$

$80$

$105$

$125$

Show answer and explanation

Answer: B

Let $a$ be adult tickets and $s$ student tickets: $a + s = 150$ and $14a + 9s = 1750$ . Substitute $s = 150 - a$ : $14a + 1350 - 9a = 1750$ , so $5a = 400$ and $a = 80$ .

Choice A is the number of student tickets.

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