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 $10\%(x-10)=20\%(x-20)$ . Solving this equation gives $x=30$ , so the answer is $\boxed{\textbf{(B) }$30}$ .

Page

Toolbox

Search

1983 AHSME Problems/Problem 7

Problem

Solution