Question

The owner of two hotels is ordering towels. He bought 24 hand towels and 5 bath towels for his hotel in Washington, spending a total of $151. He also ordered 26 hand towels and 66 bath towels for his hotel in Lancaster, spending $830. How much does each towel cost?

Answer 1

The first step is to state the system of equations that represent this situation.

Let x and y be the cost of a hand towel and a bath towel respectively.

The equation that represents the money spent for the towels of the hotel in Washington is:

`24x+5y=151`

The equation that represents the money spent for the towels of the hotel in Lancaster is:

`26x+66y=830`

Solve the given system of equations by equalization:

`\begin{gathered} y=(151-24x)/(5) \\ y=(830-26x)/(66) \\ (151-24x)/(5)=(830-26x)/(66) \\ 66(151-24x)=5(830-26x) \\ 9966-1584x=4150-130x \\ 1584x-130x=9966-4150 \\ 1454x=5816 \\ x=(5816)/(1454) \\ x=4 \end{gathered}`

It means that a hand towel costs $4.

Use this value to find y:

`\begin{gathered} y=(151-24(4))/(5) \\ y=(151-96)/(5) \\ y=(55)/(5) \\ y=11 \end{gathered}`

A bath towel costs $11.