Question

6. The school volleyball team is selling t-shirts and baseball hats as a fundraiser for their

program. The t-shirts are selling for $15 each and the baseball hats are selling for $12
each. If the school volleyball-team sold a total of 84-items for a total of $1146, determine-
how many of each item they sold.

Answer 1

Let x represent the number of t-shirts sold, and y represent the number of baseball hats sold. We can create the following system of linear equations to represent this problem:

15x + 12y = 1146

x + y = 84

To solve this system of equations, we can first solve for x in the second equation by subtracting y from both sides:

x = 84 - y

Substituting this expression for x in the first equation, we get:

15(84 - y) + 12y = 1146

Expanding the left side of the equation gives us:

1260 - 15y + 12y = 1146

Combining like terms on the left side gives us:

1260 - 3y = 1146

Adding 3y to both sides gives us:

1260 = 1146 + 3y

Subtracting 1146 from both sides gives us:

114 = 3y

Dividing both sides by 3 gives us:

38 = y

Substituting this value for y in the equation x = 84 - y, we get:

x = 84 - 38

Simplifying this equation gives us:

x = 46

Therefore, the school volleyball team sold 46 t-shirts and 38 baseball hats.