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:
[tex]24x+5y=151[/tex]
The equation that represents the money spent for the towels of the hotel in Lancaster is:
[tex]26x+66y=830[/tex]
Solve the given system of equations by equalization:
[tex]\begin{gathered} y=\frac{151-24x}{5} \\ y=\frac{830-26x}{66} \\ \frac{151-24x}{5}=\frac{830-26x}{66} \\ 66(151-24x)=5(830-26x) \\ 9966-1584x=4150-130x \\ 1584x-130x=9966-4150 \\ 1454x=5816 \\ x=\frac{5816}{1454} \\ x=4 \end{gathered}[/tex]
It means that a hand towel costs $4.
Use this value to find y:
[tex]\begin{gathered} y=\frac{151-24(4)}{5} \\ y=\frac{151-96}{5} \\ y=\frac{55}{5} \\ y=11 \end{gathered}[/tex]
A bath towel costs $11.
