Question

Rowan bought some vanilla and chocolate cupcakes in the ratio of 5:4. After Rowan’s classmates ate an equal number of the two types of cupcakes, there were 40% fewer chocolate than vanilla cupcakes. In the end, there were 152 cupcakes left. How many cupcake of each type were eaten?

Answer 1

Vanilla: Chocolate
5 ||||||||||| 4
after eating equal number of vanilla and chocolate
chocolate = 60% vanilla (40% left means equal to 60%)
chocolate = 3/5 vanilla
vanilla/chocolate = 5/3
it means after eating (5 + 3) = 8 = 8 units are left
8 units = 152
1 unit = 19
Vanilla = 19 * 5 = 95
Chocolate = 19 * 3 = 57
if x unit are eaten then
(95 + x)/(57 + x) = 5/4
380 + 4x = 285 + 5x
=> x = 95
95 units of both vanilla and chocolate were eaten.