Question

A box of Munchkins contains chocolate and glazed donut holes. If Jacob ate 2 chocolate

Munchkins, then 1/11 of the remaining Munchkins would be chocolate. If he instead added 4
glazed Munchkins to the original box, 1/7 of the Munchkins would be chocolate. How many total
Munchkins are in the original box?

Answer 1

24 munchkins.

Step-by-step explanation:

Let C be the number of chocolate and D be number of glazed donut holes in the original box.

We are told if Jacob ate 2 chocolate munchkins, then 1/11 of the remaining Munchkins would be chocolate. We can represent this information as:

`C-2=(1)/(11)*(C+D-2)...(1)`

We are also told if he instead added 4 glazed Munchkins to the original box, 1/7 of the Munchkins would be chocolate. We can represent this information as:

`C=(1)/(7)*(C+D+4)...(2)`

Upon substituting C's value from equation (2) in equation (1) we will get,

`(1)/(7)*(C+D+4)-2=(1)/(11)*(C+D-2)`

Let us have a common denominator on right side of equation.

`(1)/(7)*(C+D+4)-(7*2)/(7)=(1)/(11)*(C+D-2)`

`(C+D+4-14)/(7)=(1)/(11)*(C+D-2)`

Multiplying both sides of our equation by 7, we will get,

`7*(C+D-10)/(7)=7*(1)/(11)*(C+D-2)`

`C+D-10=(7)/(11)*(C+D-2)`

Multiplying both sides of our equation by 11, we will get,

`11*(C+D-10)=11*(7)/(11)*(C+D-2)`

`11*(C+D-10)=7*(C+D-2)`

`11C+11D-110=7C+7D-14`

`11C-7C+11D-7D=-14+110`

`4C+4D=96`

`4(C+D)=96`

`(C+D)=(96)/(4)`

`(C+D)=24`

Therefore, the total number of Munchkins in original box is 24.