Chapter 6.7, Problem 39PPS

To determine

To find: Total number of movies and games rented.

Answer to Problem 39PPS

Here $5$ movies and $3$ video games were rented.

Explanation of Solution

Given:

Rent of one movie is $\$4$

Rent of one game is $\$4.50$

M and his sisters spent $\$33.50$ .

Calculation:

Let $u$ movies and $p$ video games be rented.

Since M and his sisters rented 2 items each at the video store, thus total $4\times 2=8$ were rented.

This gives $u+p=8$ .

Rent of one movie is $\$4$ and rent of one game is $\$4.50$ . M and his sisters spent $\$33.50$ , this gives $4u+4.50p=33.50$ .

Thus the system of equation is

  $u+p=8$

  $4u+4.50p=33.50$

Solve the system of equations

  $\begin{array}{l}u+p=8\text{ Multiply by 4 }\Rightarrow \text{ 4u + 4p = 32}\\ 4u+4.50p=33.50\Rightarrow \text{ 4u + 4}\text{.50p = 33}\text{.50}\\ \text{ \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_}\\ \text{ subtract }\Rightarrow \text{ - 0}\text{.50p = -1}\text{.50}\\ \Rightarrow \text{ p = 3}\end{array}$

Put the value of $p$ in first equation

  $\begin{array}{l}\Rightarrow \text{ u + 3 = 8}\\ \Rightarrow \text{ u = 8 - 3}\\ \Rightarrow \text{ u = 5 }\end{array}$

Hence $5$ movies and $3$ video games were rented.

Conclusion:

Therefore, $5$ movies and $3$ video games were rented.