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?

1 Answer
Mar 7, 2018

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

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

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

6a = 17.73 - 3n

so;

a = (17.73 - 3n)/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;

5n + 3(3n-17.73)/6 = 13.24

we can reduce the fraction 3/6 to 1/2;

5n + (3n-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 = (17.73 - 3n)/6

so,

a = (17.73 - 3(3.40))/6

finally;

a = $1.26