MathDB
Soda is not healthy

Source: 2017 AMC10 #14

February 8, 2017
AMCAMC 10percent2017 AMC 10A

Problem Statement

Every week Roger pays for a movie ticket and a soda out of his allowance. Last week, Roger's allowance was AA dollars. The cost of his movie ticket was 20%20\% of the difference between AA and the cost of his soda, while the cost of his soda was 5%5\% of the difference between AA and the cost of his movie ticket. To the nearest whole percent, what fraction of AA did Roger pay for his movie ticket and soda?
<spanclass=latexbold>(A)</span>9%<spanclass=latexbold>(B)</span>19%<spanclass=latexbold>(C)</span>22%<spanclass=latexbold>(D)</span>23%<spanclass=latexbold>(E)</span>25% <span class='latex-bold'>(A) </span>9\%\qquad <span class='latex-bold'>(B) </span> 19\%\qquad <span class='latex-bold'>(C) </span> 22\%\qquad <span class='latex-bold'>(D) </span> 23\%\qquad <span class='latex-bold'>(E) </span>25\%