Question

The owner of two hotels is ordering towels. He bought 15 hand towels and 43 bath towels for his hotel in Livingston, spending a total of $548. He also ordered 99 hand towels and 62 bath towels for his hotel in Lancaster, spending $1,177. How much does each towel cost?

Answer 1

Answer:

The cost of each Hand towels is $5 and Cost of each Bath towel is $11.

Step-by-step explanation:

Let the Cost of Each hand Towels be $'x'$.

Let the Cost of Each Bath Towels be $'y'$.

Now Given:

15 hand towels and 43 bath towels for his hotel in Livingston, spending a total of $548.

So we can say that;

$15x+43y=548$

$15x=548-43y\\\\x=\frac{548-43y}{15}$  ⇒ Equation 1

Also Given:

99 hand towels and 62 bath towels for his hotel in Lancaster, spending $1,177.

So we can say that;

$99x+62y =1177$  ⇒ Equation 2

Substituting the value of 'x' from equation 1 in Equation 2 we get;

$99\frac{(548-43y)}{15}+62y=1177\\\\33\frac{(548-43y)}5+62y=1177\\\\\frac{18084-1419y}5+62y=1177$

Now taking LCM to make the denominator common we get;

$\frac{18084-1419y}5+\frac{62y\times5}{5}=1177\\\\\frac{18084-1419y}5+\frac{310y}5=1177\\\\\frac{18084-1419y+310y}{5}=1177$

$18084-1109y=1177\times5\\\\18084-1109y=5885$

Combining the like terms we get;

$18084-5885=1109y\\\\12199=1109y$

Dividing both side by 1109 we get;

$\frac{12199}{1109}=\frac{1109y}{1109}\\\\y=\ 11$

Substituting the value of y in equation 1 we get;

$x=\frac{548-43y}{15}=\frac{548-43\times11}{15}=\ 5$

Hence The cost of each Hand towels is $5 and Cost of each Bath towel is $11.