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?

Mercedes bought 22 cupcakes

Explanation

Let number of vanilla cupcakes=x

Number of chocolate cupcakes=y

When she eats 1 vanilla cupcake

Number of vanilla cupcakes remaining=x-1

Number of cupcakes remaining=x+y-1

Given

(1/7) (x+y-1) = x-1 (1)

When she eats two chocolate cupcakes instead

Number of chocolate cupcakes remaining=y-2

Given that

(1/5) (x+y-2) = x (2)

Consider equation (1)

(1/7) (x+y-1) = x-1

x+y-1=7x-7

7x-x-y=6

6x-y=6 (3)

Consider equation (2)

(1/5) (x+y-2) = x

x+y-2=5x

5x-x-y=-2

4x-y=-2 (4) solving (3) and (4) using

elimination method we get x=4

y=18

Total number of cupcakes Mercedes bought=x+y=4+18=22