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?

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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?

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Answer 1 · 2018-03-07T21:28:46

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

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

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

$6 a = 17.73 - 3 n$ $6a = 17.73 - 3n$

so;

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

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, $a$ $a$ , of an album into an equation gives us;

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

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

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

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

$n = $ 3.40$ $n = $3.40$

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

so,

$a = \frac{17.73 - 3 (3.40)}{6}$ $a = (17.73 - 3(3.40))/6$

finally;

a = $1.26

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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?

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