Question

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?

Answer 1

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