1. ## help

At Gwen's garage sale, all books were one price, and all magazines were another price. Harriet bought four books and three magazines for $1.45, and June bought two books and five magazines for$1.25. What was the price of a book and what was the price of a magazine?

At Gwen's garage sale, all books were one price, and all magazines were another price. Harriet bought four books and three magazines for $1.45, and June bought two books and five magazines for$1.25. What was the price of a book and what was the price of a magazine?
Call the price of one book "b" and the price of one magazine "m." Then we know, from Harriet:
$4b+3m=1.45$

From June:
$2b+5m=1.25$

So, we need to solve this system of equations.

I solved the first equation for b and got:
$b=\frac{1}{4} \left ( 1.45-3m \right )$

Now, plug that value of b into the second equation:
$2 \frac{1}{4} \left ( 1.45-3m \right ) + 5m = 1.25$
which you can now solve for m. I got: m = 0.15.

You can now plug that value of m into any of the above equations to get b. I got b = 0.25.

-Dan