At a college bookstore, Carla purchased a math textbook and a novel that cost a total of $54, not including tax. If the price of the math textbook, #m#, is $8 more than 3 times the price of the novel, #n#, how much would 5 novels cost?

Question

28130 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-07-22T18:11:28

Five novels would cost #$57.50#.

Ok let's write down what we know about the system:

She bought a textbook and a novel for a total of $54, so the price of each must add together to give 54.

#m + n = 54 " "color(blue)("Equation 1")#

If the textbook costs $8 more than three novels then subtracting the cost of three novels from the cost of the text book leaves $8.

#m - 3n = 8 " "color(blue)("Equation 2")#

We now have two simultaneous equations. Subtract equation 2 from equation 1:

#(m+n) - (m-3n) = 54 - 8#

#4n = 46#

#n = 11.5#

To check from equation 1:

#m = 54 - n#

#m = 54 -11.5#

#therefore m = 42.5#

This fits which is good. The question asked for the price of five novels, so

#5n = 5*11.5 = 57.5#

Answer 2 · 2016-07-22T18:14:17

One novel costs $11.50, 5 will cost $57.50#

The prices have already been defined for us:
Price of maths book = #m# and of novel = #n#

Lets write equations for what we know before we try to solve them.
There are two variables so we need at least two equations.

#m+n= 54" cost of one of each book is "54#
#m = 3n +8" Maths book costs $8 more than 3 novels"#

We have 2 equations so we can solve for m and n.
#m = 54-n " and "m = 3n +8#

Therefore #54-n = 3n +8#

#4n = 54-8#
#4n = 46#
#n = 11.50#

If one novel costs $11.50, five will cost $57.50#

Check:
#m = 11.50xx3+8 = $42.50#
#42.50 +11.50 = $54#