Q10. - Algebra 1

Question

Jason received a \(50 gift certificate for his birthday. He wants to buy a DVD and a poster from a media store. (Assume that sales tax is included in the prices.) Write and solve a linear inequality to show how much he would have left to spend after making these purchases.

 

Weekend Blowout Sale

All DVDs only \)14.95

All CDs only \(11.25

All posters only \)10.99

Step-by-Step Solution

Answer

The amount left with Jason is $24.06.

Step 1. Assign the variables.

Let the money spent by Jason on DVDs and posters by $x$ and $y$ respectively. And the money left with Jason be $z$.

Step 2. Write the linear inequality.

Then since Jason received a $50 gift card, therefore, the inequality thus obtained will be 

$x+y+z\le 50$.

Step 3. Solve the inequality.

Since purchases were made by Jason all DVDs cost $14.95, and all posters cost $10.99. Substitute 14.95 for $x$ and 10.99 for y into the inequality $x+y+z\le 50$ and simplify.

  $$\begin{gathered} x+y+z\le 50 \\ 14.95+10.99+z\le 50 \\ \text{25.94}+z\le 50 \\ z\le 50-25.94 \\ z\le \text{24.06} \end{gathered}$$ 

Therefore, Jason would have been left with almost $24.06 to spend after making these purchases.