Chapter 6.2, Problem 39PFA

To determine

To find: Number of total jerseys did school purchased.

Answer to Problem 39PFA

Total number of jerseys school purchased = 12.

Explanation of Solution

Given information:

Amount paid for Basketball and Soccer jerseys = $248

Number of basketball jerseys = 3 times of soccer jerseys − 6

Cost of each basketball jersey = $28

Cost of each soccer jersey = $20

Let $x$ be the number of Basketball jerseys

Let $y$ be thee number of soccer jerseys

  $\Rightarrow x=3y-6$ ---------(1)

Total cost of $x$ basketball jerseys and $y$ soccer jerseys = $28x+20y$

  $\Rightarrow 248=28x+20y$ ----------(2)

Substitute value of $x$ from equation-(1) in equation-(2)

We get

  $\begin{array}{l}\Rightarrow x=3y-6\\ \Rightarrow 248=28x+20y\\ \Rightarrow 248=28\left(3y-6\right)+20y\\ \Rightarrow 28\left(3y\right)-28\left(6\right)+20y=248\\ \Rightarrow 84y-168+20y=248\\ \Rightarrow 84y+20y=248+168\\ \Rightarrow 104y=416\\ \Rightarrow y=\frac{416}{104}\\ \Rightarrow y=4\end{array}$

Substitute value of $y$ in equation-(1)

We get

  $\begin{array}{l}\Rightarrow x=3y-6\\ \Rightarrow x=3\left(4\right)-6\\ \Rightarrow x=12-6\\ \Rightarrow x=6\end{array}$

Therefore,

Total number of jerseys = number of Basketball jerseys + number of soccer jersey

Total number of jerseys = $x+y$ = $6+6=12$

Total number of Jerseys =12.