Chapter 6, Problem 12PFA

To determine

To find: The number of concert T-shirts Julia sold.

Answer to Problem 12PFA

Julia sold 23 concert T-shirts.

Explanation of Solution

Given information:

At a garage sale Julia sold a total 32 T-shirts for $114. The prices she sold the shirts for are shown in table here.

Method used:

According to given conditions a system of equations is obtained and then solved.

Calculations:

Let x and y be the number of sports T-shirts and concert T-shirts Julia sold.

Since, total shirts sold are 32, therefore,

  $x+y=32$  ...... (1)

The selling price of x sports T-shirts is $ 5x and that of y concert T-shirts is $ 3y .The total amount collected by selling both kinds of T- shirts is $114, therefore,

  $5x+3y=114$  ...... (2)

Now, multiplying equation (1) by 5 and subtracting from equation (2)

  $\left(5x+3y\right)-5\left(x+y\right)=114-5\times 32$

  $\Rightarrow 5x+3y-5x-5y=114-160$

  $\Rightarrow \cancel{5x}+3y-\cancel{5x}-5y=46$

  $\Rightarrow -2y=-46$

  $\Rightarrow y=\frac{-46}{-2}=23$

Thus, Julia sold 23 concert T-shirts.

Conclusion:

Julia sold 23 concert T-shirts.