Let [tex]s[/tex] be the number of strawberry cupcakes, and [tex]c[/tex] the number of chocolate cupcakes.
From our problem we know that the total number of cupcakes is 180, so [tex]c+s=180[/tex]. We also know that the number of chocolate cupcakes is eighteen more than twice the number of strawberry cupcakes, so [tex]c-18=2s[/tex], or solving for [tex]c[/tex]: [tex]c=2s+18[/tex].
Know we have our system of equations:
[tex] \left \{ {{c+s=180} \atop {c=2s+18}} \right. [/tex]
We can conclude that the correct answer is 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 [tex]c=2s+18[/tex]; lets replace that value in our first equation to find the number of strawberry cupcakes:
[tex]2s+18+2=180[/tex]
[tex]3s=162[/tex]
[tex]s= \frac{162}{3} [/tex]
[tex]s=54[/tex]
Now that we know the number of strawberry cupcakes, lets replace that value in our second equation to find the number of chocolate cupcakes:
[tex]c=2(54)+18[/tex]
[tex]c=108+18[/tex]
[tex]c=126[/tex]
As a bonus, we can conclude that the math club have 126 chocolate cupcakes and 54 strawberry cupcakes.
