1983 AHSME Problems/Problem 7

Problem

Alice sells an item at $\$10$ less than the list price and receives $10\%$ of her selling price as her commission. Bob sells the same item at $\$20$ less than the list price and receives $20\%$ of his selling price as his commission. If they both get the same commission, then the list price is

$\textbf{(A) } \$20\qquad \textbf{(B) } \$30\qquad \textbf{(C) } \$50\qquad \textbf{(D) } \$70\qquad \textbf{(E) } \$100$

Solution

If $x$ is the list price, then $0.1(x-10)=0.2(x-20)$ . Solving this equation gives $x=30$ , so the answer is $\boxed{\textbf{(B) }\$30}$ .

1983 AHSME (Problems • Answer Key • Resources)
Preceded by Problem 6	Followed by Problem 8
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30
All AHSME Problems and Solutions

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1983 AHSME Problems/Problem 7

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