# I buy 5 notebooks and 3 albums spending $13.24, then I buy another 3 books and 6 albums spending$17.73. How much does each book and album cost?

Mar 7, 2018

Set the books and albums to variables to get two equations such that;

$5 n + 3 a = 13.24$
and
$3 n + 6 a = 17.73$

There's not much that we can do with those in their current state, so let's re-write one of them.

$6 a = 17.73 - 3 n$

so;

$a = \frac{17.73 - 3 n}{6}$

Hey look! We just found the price of an album with respect to the price of a notebook! Now that we can work with! Plugging the price, $a$, of an album into an equation gives us;

$5 n + 3 \frac{3 n - 17.73}{6} = 13.24$

we can reduce the fraction $\frac{3}{6}$ to $\frac{1}{2}$;

$5 n + \frac{3 n - 17.73}{2} = 13.24$

Now solve for $n$ to find the exact price of an notebook;

n = $3.40 With the exact price of a notebook found, finding the price of an album is as simple as plugging $n$into any equation that has both $a$and $n$in it. I think I'll choose, $a = \frac{17.73 - 3 n}{6}$so, $a = \frac{17.73 - 3 \left(3.40\right)}{6}$finally; a =$1.26