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?

She bought 22 number of cupcakes.

Step-by-step 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

⇒ 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

⇒ 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)

step-by-step explanation:

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