A school spent $150 on advertising for a breakfast fundraiser. Each plate of food was sold for $8.00 but cost the school $2.00 to prepare. After all expenses were paid, the school raised $2,400 at the fundraiser. Which equation can be used to find x, the number of plates that were sold?
Set up the cost equation C(x) where x is the number of plates sold:
C(x) = Cost per plate * x plates
C(x) = 2x
Set up the revenue equation R(x) where x is the number of plates sold:
R(x) = Sales price per plate * x plates
C(x) = 8x
Set up the profit equation P(x) where x is the number of plates sold:
P(x) = R(x) - C(x)
P(x) = 8x - 2x
P(x) = 6x
We're told the profits P(x) for the fundraiser were $2,400, so we set 6x equal to 2400 and solve for x:
6x = 2400
To solve this equation for x, we type it in our math engine and we get:
x =400 plates
Set up the cost equation C(x) where x is the number of plates sold:
C(x) = Cost per plate * x plates
C(x) = 2x
Set up the revenue equation R(x) where x is the number of plates sold:
R(x) = Sales price per plate * x plates
C(x) = 8x
Set up the profit equation P(x) where x is the number of plates sold:
P(x) = R(x) - C(x)
P(x) = 8x - 2x
P(x) = 6x
We're told the profits P(x) for the fundraiser were $2,400, so we set 6x equal to 2400 and solve for x:
6x = 2400
To solve this equation for x, we type it in our math engine and we get:
x =400 plates