Question

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

Answer 1

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