Respuesta :
Answer:
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:
[tex]C-2=\frac{1}{11}*(C+D-2)...(1)[/tex]
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:
[tex]C=\frac{1}{7}*(C+D+4)...(2)[/tex]
Upon substituting C's value from equation (2) in equation (1) we will get,
[tex]\frac{1}{7}*(C+D+4)-2=\frac{1}{11}*(C+D-2)[/tex]
Let us have a common denominator on right side of equation.
[tex]\frac{1}{7}*(C+D+4)-\frac{7*2}{7}=\frac{1}{11}*(C+D-2)[/tex]
[tex]\frac{C+D+4-14}{7}=\frac{1}{11}*(C+D-2)[/tex]
Multiplying both sides of our equation by 7, we will get,
[tex]7*\frac{C+D-10}{7}=7*\frac{1}{11}*(C+D-2)[/tex]
[tex]C+D-10=\frac{7}{11}*(C+D-2)[/tex]
Multiplying both sides of our equation by 11, we will get,
[tex]11*(C+D-10)=11*\frac{7}{11}*(C+D-2)[/tex]
[tex]11*(C+D-10)=7*(C+D-2)[/tex]
[tex]11C+11D-110=7C+7D-14[/tex]
[tex]11C-7C+11D-7D=-14+110[/tex]
[tex]4C+4D=96[/tex]
[tex]4(C+D)=96[/tex]
[tex](C+D)=\frac{96}{4}[/tex]
[tex](C+D)=24[/tex]
Therefore, the total number of Munchkins in original box is 24.
