Question

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 $\tfrac34$ 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?

$30$

$32$

$36$

$40$

$50$

Solution:

Let a regular lemonade hold $a$ ounces, so Ann's large holds $\tfrac32 a.$ After each drinks $\tfrac34,$ Ann has $\tfrac14\cdot\tfrac32 a = \tfrac38 a$ left, and she gives Ed $\tfrac13\cdot\tfrac38 a + 2 = \tfrac18 a + 2$ ounces.

Ed drinks his full $a$ ounces plus that gift, and Ann drinks her $\tfrac32 a$ minus the gift. Setting these equal, $a + \left(\tfrac18 a + 2\right) = \tfrac32 a - \left(\tfrac18 a + 2\right),$ which gives $4 = \tfrac14 a,$ so $a = 16.$

Then Ed drank $16$ ounces and Ann drank $24$ ounces, for a total of $40$ ounces.

Thus, the correct answer is D.

2014 AMC 12B Problem 6

Solution:

Problem 6 in Other Years