For a fundrasier, the Best Buddies club sold t-shirts. The adult shirts were $15 per shirt and the youth shirts were $12 per shirt, and they made a total of $330 on the shirts. If they sold a total of 26 shirts, how many of each did they sell?
I don't understand this, so please show work.
A + Y = 26, so Y = 26 - A
15A + 12Y = 330
Substitute 26-A for Y in second equation and solve for A. Insert that value into the first equation and solve for Y. Check by inserting both values into the second equation.
I don't understand the substitute part.
To solve this problem, we can use a system of equations. Let's assume that x represents the number of adult shirts sold and y represents the number of youth shirts sold.
We know that the price of each adult shirt is $15, so the total revenue from adult shirts can be represented as 15x. Similarly, the total revenue from youth shirts can be represented as 12y.
According to the problem, the total revenue from all the shirts is $330, so we can set up the equation:
15x + 12y = 330 ----(Equation 1)
We also know that the total number of shirts sold is 26, which gives us another equation:
x + y = 26 ----(Equation 2)
Now we have a system of equations with two variables:
15x + 12y = 330 ----(Equation 1)
x + y = 26 ----(Equation 2)
We can solve this system of equations using substitution or elimination method. Let's solve it using the elimination method:
Multiply Equation 2 by 15:
15(x + y) = 15(26)
15x + 15y = 390 ----(Equation 3)
Now, subtract Equation 3 from Equation 1 to eliminate x:
(15x + 12y) - (15x + 15y) = 330 - 390
-3y = -60
Divide both sides of the equation by -3:
y = -60 / -3
y = 20
Now, substitute the value of y into Equation 2 to solve for x:
x + 20 = 26
x = 26 - 20
x = 6
Therefore, they sold 6 adult shirts and 20 youth shirts.