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?

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