2014 AMC 12B Problems/Problem 6

Problem

Ed and Ann both have lemonade with their lunch. Ed orders the regular size. Ann gets the large lemonade, which is 50% more than the regular. After both consume of their drinks, Ann gives Ed a third of what she has left, and 2 additional ounces. When they finish their lemonades they realize that they both drank the same amount. How many ounces of lemonade did they drink together?

$\textbf{(A)}\ 30\qquad\textbf{(B)}\ 32\qquad\textbf{(C)}\ 36\qquad\textbf{(D)}}\ 40\qquad\textbf{(E)}\ 50$ (Error compiling LaTeX. Unknown error_msg)

Solution

Let the size of Ed's drink equal ounces, and let the size of Ann's drink equal ounces. After both consume of their drinks, Ed and Ann have and ounces of their drinks remaining. Ann gives away ounces to Ed.

In the end, Ed drank everything in his original lemonade plus what Ann gave him, and Ann drank everything in her original lemonade minus what she gave Ed. Thus we have The total amount the two of them drank is simply