Question

Helen and Althea went shopping for towels to take to college. Helen bought 4 bath towels and 3 hand towels for $72 while Althea bought 3 bath towels and 6 hand towels of the same kind for $84.How much did 1 bath towel cost?

Answer 1

For the given problem

Let one bath towel costs x

And one hand towel cost y

Helen bought 4 bath towels and 3 hand towels for $72

so,

$4x+3y=72\rightarrow(1)$

Althea bought 3 bath towels and 6 hand towels of the same kind for $84

So,

$3x+6y=84\rightarrow(2)$

Solve the equations (1) and (2) to find x and y

Multiply equation (1) by (-2) then add to equation (2) to cross y

then solve for x

$\begin{gathered} 4x+3y=72\rightarrow(\times-2) \\ 3x+6y=84 \\ ============== \\ -8x-6y=-144 \\ 3x+6y=84 \\ ============== \\ -5x=-60 \\ x=\frac{-60}{-5}=12 \end{gathered}$

Substitute with x into equation (1) to find y

$\begin{gathered} 4\cdot12+3y=72 \\ 3y=24 \\ y=\frac{24}{3}=8 \end{gathered}$

So, the answer will be:

The cost of one bath towel = $12

The cost of one hand towel = $8