Respuesta :
Let h and b be the cost for the hand towels and bath towels, respectively. Then, the statement "39 hand towels and 43 bath towels for $426" can be written as
[tex]39h+43b=426[/tex]and the statement "35 hand towels and 97 bath towels for $908" can be written as
[tex]35h+97b=908[/tex]So, we have the following system of equations:
[tex]\begin{gathered} 39h+43b=426 \\ 35h+97b=908 \end{gathered}[/tex]Solving by elimination method.
By multiplying the first equation by -35 and the second one by 39, we have an equivalent system of equations:
[tex]\begin{gathered} -1365h-1505b=-14910 \\ 1365h+3783b=35412 \end{gathered}[/tex]So, we can eliminate variable h by adding both equations, that is,
[tex]2278b=20502[/tex]Then, we have
[tex]\begin{gathered} b=\frac{20502}{2278} \\ b=9 \end{gathered}[/tex]Finally, by substituting this result into the first equation, we get
[tex]39h+43(9)=426[/tex]which gives
[tex]\begin{gathered} 39h+387=426 \\ 39h=39 \\ \text{then} \\ h=\frac{39}{39} \\ h=1 \end{gathered}[/tex]Therefore, the cost for the hand towels is $1 and for the bath towels is $9.
