Respuesta :
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 [tex]'x'[/tex].
Let the Cost of Each Bath Towels be [tex]'y'[/tex].
Now Given:
15 hand towels and 43 bath towels for his hotel in Livingston, spending a total of $548.
So we can say that;
[tex]15x+43y=548[/tex]
[tex]15x=548-43y\\\\x=\frac{548-43y}{15}[/tex]  ⇒ Equation 1
Also Given:
99 hand towels and 62 bath towels for his hotel in Lancaster, spending $1,177.
So we can say that;
[tex]99x+62y =1177[/tex]  ⇒ Equation 2
Substituting the value of 'x' from equation 1 in Equation 2 we get;
[tex]99\frac{(548-43y)}{15}+62y=1177\\\\33\frac{(548-43y)}5+62y=1177\\\\\frac{18084-1419y}5+62y=1177[/tex]
Now taking LCM to make the denominator common we get;
[tex]\frac{18084-1419y}5+\frac{62y\times5}{5}=1177\\\\\frac{18084-1419y}5+\frac{310y}5=1177\\\\\frac{18084-1419y+310y}{5}=1177[/tex]
[tex]18084-1109y=1177\times5\\\\18084-1109y=5885[/tex]
Combining the like terms we get;
[tex]18084-5885=1109y\\\\12199=1109y[/tex]
Dividing both side by 1109 we get;
[tex]\frac{12199}{1109}=\frac{1109y}{1109}\\\\y=\$11[/tex]
Substituting the value of y in equation 1 we get;
[tex]x=\frac{548-43y}{15}=\frac{548-43\times11}{15}=\$5[/tex]
Hence The cost of each Hand towels is $5 and Cost of each Bath towel is $11.
