Question

Mercedes bought some vanilla cupcakes and some chocolate cupcakes. If she

eats one of the vanilla cupcakes, then 1/7 of the remaining cupcakes will be
vanilla. If Mercedes instead eats two of the chocolate cupcakes, then 1/5 of the
remaining cupcakes will be vanilla. How many cupcakes did Mercedes buy?

Answer 1

She bought 22 number of cupcakes.

Explanation:

Let Mercedes bought x number of vanilla cupcakes and y number of chocolate cupcakes.

If she eats one of the vanilla cupcakes, then 1/7 of the remaining cupcakes will be vanilla.

So, we can write
`(1)/(7) (x + y - 1) = (x - 1)`

⇒ x + y - 1 = 7x - 7

⇒ 6x - y = 6 ......... (1)

Now, if Mercedes instead eats two of the chocolate cupcakes, then 1/5 of the remaining cupcakes will be vanilla.

So, we can write
`(1)/(5)(x + y - 2) = x`

⇒ x + y - 2 = 5x

⇒ 4x - y = - 2 ............ (2)

Now, solving equations (1) and (2) we get

(6x - 4x) = 6 - ( - 2) = 8

⇒ 2x = 8

⇒ x = 4

Then, from equation (2) we get, y = 4x + 2 = 18

Therefore, she bought (18 + 4) = 22 number of cupcakes. (Answer)