Question

On a website selling books, three paperback books and five hardcover books cost $80.10, and seven paperback books and four hardcover books cost $100.65. What is the total cost of one paperback and one hardcover book?

Answer 1

To answer this kind of question, you need to insert the first equation into second equation or vice versa. The equation from the question should be:

1. 3 paperback books +  5 hardcover book = $80.10
2. 7 paperback books + 4 hardcover book= $100.65

It would be easier to convert the 1st equation into
5 hardcover book = $80.10- 3 paperback books
hardcover book= $16.02- 0.6 paperback books

Then insert it to 2nd equation:
7 paperback books + 4 ($16.02- 0.6 paperback books)= $100.65
7 paperback books + $64.08- 2.4 paperback books= $100.65
4.6 paperback books = $100.65-  $64.08= $36.57
paperback book= $7.95

Insert paperback book price to the first equation to find the hardcover book price
3 paperback books +  5 hardcover book = $80.10
3 ($7.95)+  5 hardcover book = $80.10
5 hardcover book = $80.10 - $23.85= $56.25
hardcover book = $11.25

Then one paperback and one hardcoverbook= $7.95 + $11.25= $19.20