4 books and 5 magazines cost $103.60 altogether. 8 books and 3 magazines cost $134.40 altogether. How much less does each magazine cost than each book?

Question

4 books and 5 magazines cost $103.60 altogether. 8 books and 3 magazines cost $134.40 altogether. How much less does each magazine cost than each book?

Answer 1

In order to solve this problem, the assumption has to be made that the price of books and magazines are both uniform. If x = the price of books and y = the price of magazines, then we have:

 

4x + 5y = 103.60

8x + 3y = 134.40

 

This system of equations can be solved by various methods. I will choose the Elimination Method. Let's multiply the top equation by 2, and then subtract.

 

   8x + 10y = 207.20

- (8x + 3y = 134.40)

 

7y = 72.8

y = 10.4 or $10.40 = the price of magazines

 

Now, plug this value of y into either of our original equations

 

4x + 5(10.40) = 103.60

4x + 52 = 103.60

4x = 51.6

x = 12.9 or $12.90 = cost of books

 

The difference in price between books and magazines is $12.90 - $10.40 = $2.50