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 in dollars 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 $10\%(x-10)=20\%(x-20)$ . Solving this, you get $x=30$ . So the answer is $\boxed{\textbf{(B) }30}$

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1983 AHSME Problems/Problem 7

Problem

Solution