1953 AHSME Problems/Problem 1

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A boy buys oranges at $3$ for $10$ cents. He will sell them at $5$ for $20$ cents. In order to make a profit of $$ (Error compiling LaTeX. Unknown error_msg)1.00$, he must sell:$\textbf{(A)}\ 67 \text{ oranges} \qquad \textbf{(B)}\ 150 \text{ oranges} \qquad \textbf{(C)}\ 200\text{ oranges}\ \textbf{(D)}\ \text{an infinite number of oranges}\qquad \textbf{(E)}\ \text{none of these}$Solution:

The boy buys$ (Error compiling LaTeX. Unknown error_msg)3$oranges for$10$cents or$1$orange for$\frac{10}{3}$cents.  He sells them at$\frac{20}{5}=4$cents each.   That means for every orange he sells, he makes a profit of$4-\frac{10}{3}=\frac{2}{3}$cents.

To make a profit of$ (Error compiling LaTeX. Unknown error_msg)100$cents, he needs to sell$\frac{100}{\frac{2}{3}}=\boxed{150}=\boxed{\text{B}}$

~mathsolver101