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 $54

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?

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Luna 2 weeks 2021-11-15T13:19:04+00:00 1 Answer 0 views 0

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    2021-11-15T13:20:39+00:00

    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.

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