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.

Answer 1

Let b be the price of the bath towels and h be price of the hand towels. For Helen, we can write the following equation

$4b+3h=72$

And for Althea, we have

$3b+6h=84$

Then, we have 2 equations in 2 unknowns. By multipliying the first equation by -2, we have the following equivalent system of equation

$\begin{gathered} -8b-6h=-144 \\ 3b+6h=84 \end{gathered}$

By adding both equations, we have

$\begin{gathered} -5b+0=-60 \\ or \\ -5b=-60 \end{gathered}$

Then, b is given by

$\begin{gathered} b=\frac{-60}{-5} \\ b=12 \end{gathered}$

Therefore, 1 bath towel cost $12, which corresponds to option 3