Respuesta :
Answer:
we need numbers to answer the question
Step-by-step explanation:
Here is the full question
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?
Answer:
22
Step-by-step explanation:
Let represent the number of vanilla cupcakes=v
and the number of chocolate cupcakes=c
So, total number of cupcakes Mercedes bought = (v+c)
When she eats 1 vanilla cupcake
Number of vanilla cupcakes remaining=v-1
Number of cupcakes remaining=v+c-1
However;
[tex]\frac{1}{7}(v+c-1) = v- 1[/tex] -------------------- equation 1
If Mercedes instead eats two of the chocolate cupcakes
Number of chocolate cupcakes remaining=c-2
However
[tex]\frac{1}{5}(v+c-2) = v[/tex] --------------------- equation 2
From equation (1)
[tex]\frac{1}{7}(v+c-1) = v- 1[/tex]
[tex]v+c-1 = 7(v-1)[/tex]
[tex]v+c -1 = 7v -7[/tex]
[tex]c-1+7 = 7v -v[/tex]
[tex]c+6 = 6v[/tex]
[tex]6 = 6v - c[/tex]
[tex]6v-c = 6[/tex] --------------------- equation (3)
From equation(2)
[tex]\frac{1}{5}(v+c-2) = v[/tex]
[tex]v+c-2 =5v[/tex]
[tex]c-2 = 5v-v[/tex]
[tex]c-2 =4v[/tex]
[tex]-2 = 4v-c[/tex]
[tex]4v-c = -2[/tex] --------------------- equation (4)
equating equation (3) and (4); we have:
[tex]6v-c = 6[/tex]
[tex]4v-c = -2[/tex]
Subtracting equation (3) from (4); we have:
[tex]6v-c = 6[/tex]
- [tex]4v-c = -2[/tex]
[tex]2v[/tex] [tex]= 8[/tex]
[tex]v=\frac{8}{2}[/tex]
[tex]v=4[/tex]
From equation (3); let's replace v=4 in order to solve for c
[tex]6v-c = 6[/tex]
6(4) -c = 6
24 -c = 6
-c = 6 - 24
-c = - 18
c = 18
Total number of cupcakes Mercedes bought=v+c
=4+18
=22