Let
![s](https://tex.z-dn.net/?f=s)
be the number of strawberry cupcakes, and
![c](https://tex.z-dn.net/?f=c)
the number of chocolate cupcakes.
From our problem we know that the total number of cupcakes is 180, so
![c+s=180](https://tex.z-dn.net/?f=c%2Bs%3D180)
. We also know that the number of chocolate cupcakes is eighteen more than twice the number of strawberry cupcakes, so
![c-18=2s](https://tex.z-dn.net/?f=c-18%3D2s)
, or solving for
![c](https://tex.z-dn.net/?f=c)
:
![c=2s+18](https://tex.z-dn.net/?f=c%3D2s%2B18)
.
Know we have our system of equations:
![\left \{ {{c+s=180} \atop {c=2s+18}} \right.](https://tex.z-dn.net/?f=%20%5Cleft%20%5C%7B%20%7B%7Bc%2Bs%3D180%7D%20%5Catop%20%7Bc%3D2s%2B18%7D%7D%20%5Cright.%20)
We can conclude that the correct answer is <span>
B. c + s = 180 c = 2s + 18.
Lets solve our equations to find how many cupcakes of each they have:
from our second equation we know that </span>
![c=2s+18](https://tex.z-dn.net/?f=c%3D2s%2B18)
; lets replace that value in our first equation to find the number of strawberry cupcakes:
![2s+18+2=180](https://tex.z-dn.net/?f=2s%2B18%2B2%3D180)
![3s=162](https://tex.z-dn.net/?f=3s%3D162)
![s= \frac{162}{3}](https://tex.z-dn.net/?f=s%3D%20%5Cfrac%7B162%7D%7B3%7D%20)
![s=54](https://tex.z-dn.net/?f=s%3D54)
<span>Now that we know the number of strawberry cupcakes, lets replace that value in our second equation to find the number of chocolate cupcakes:
</span>
![c=2(54)+18](https://tex.z-dn.net/?f=c%3D2%2854%29%2B18)
![c=108+18](https://tex.z-dn.net/?f=c%3D108%2B18)
![c=126](https://tex.z-dn.net/?f=c%3D126)
As a bonus, we can conclude that the <span>math club have 126 chocolate cupcakes and 54 strawberry cupcakes. </span>