Raheem bought 9 shirts that were each the same price. He used a coupon for 54 off the entire purchase. The cost for the entire purchase after using the coupon was 108. What was the original price, in dollars, for 1 shirt?

Raheem bought 9 shirts that were each the same price. He used a coupon for 54 off the... | SAT Linear equations in one variable Practice

Context: Raheem bought $9$ shirts at the same original price each, used a coupon worth $\$ 54 $off the entire purchase, and paid$ $108$ after the coupon. We need the original price of one shirt.

Answer: 18

Why: Let $p$ be the original price of one shirt in dollars. The $9$ shirts originally cost $9p$ ; after the $\$ 54 $coupon the purchase cost$ 9p - 54 $. Set that equal to the amount paid:$ 9p - 54 = 108 $. Add$ 54 $to both sides:$ 9p = 162 $. Divide by$ 9 $:$ p = \dfrac{162}{9} = 18$.

Verification: Nine shirts at $\$ 18 $cost$ 9 \times 18 = $162 $; subtracting the$ $54 $coupon gives$ $162 - $54 = $108$, exactly what Raheem paid.

Common slips: Dividing $\$ 108 $by$ 9 $to get$ $12 $, which ignores that the coupon had already reduced the total, or applying the$ $54$ per shirt rather than to the entire purchase.

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SAT Linear equations in one variable practice question

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