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