Chapter 8.8, Problem 22E

To determine

To write and solve:

A system of equations to find the number of each item rented.

Answer to Problem 22E

The owner rented 10 inline skates and 15 bicycles.

Explanation of Solution

Given:

A business rents in-line skates and bicycles to tourists on vacation. A pair of skates rents for $15 per day. A bicycle rents for $20 per day. On a certain day, the owner of the business has 25 rentals and takes in $450.

Calculation:

Let x represent number of in-line skates and y represent number of bicycles rented.

We have been given that ona certain day, the owner of the business has 25 rentals, so number of rented skates and bicycles will be equal to 25. We can represent this information in an equation as:

  $x+y=\mathrm{25...}(1)$

A pair of skates rents for $15 per day, so amount earned from rentingxinline skates would be $15x$ .

A bicycle rents for $20 per day, so amount earned from renting ybicycles would be $20y$ .

Since the owner earned $450 from renting the items, so total amount earned from renting x pairs of skates and y bicycles should be equal to $450.We can represent this information in an equation as:

  $15x+20y=\mathrm{450...}(2)$

Now we will use substitution method to solve our system of equations. From equation (1), we will get:

  $x=25-y$

Upon substituting this value in equation (2), we will get:

  $\begin{array}{l}15x+20y=450\\ 15(25-y)+20y=450\left(\text{Substituting }x=25-y\right)\\ 375-15y+20y=450\left(\text{Using distributive property}\right)\\ 375+5y=450\left(\text{Combining like terms}\right)\\ 375375+5y=450-375\left(\text{Subtacting }375\text{from both sides}\right)\\ 5y=75\\ \frac{5y}{5}=\frac{75}{5}\left(\text{Dividing both sides by }5\right)\\ y=15\end{array}$

Therefore, 15 bicycles were rented.

Now we will substitute $y=15$ in equation (1) as:

  $\begin{array}{l}x+y=25\\ x+15=25\\ x+15-15=25-15\\ x=10\end{array}$

Therefore, 10 in-line skates were rented.