The local bookstore is having a sale on used books. Nate bought 3 hardcover books and 7 paperback books and spent $29.50. Tia bought 2 hardcover books and 5 paperback books and spent $20.50. What is the cost of a hardcover book?

Let hardcover be H

let paperback be P

3H+7P=29.5

2H+5P=20.50

now you can solve above equation and get the price of H

2H+5P=20.5

5p=20.5 - 2H

dividing both side by 5 we get

p=4.1 minus 0.4H

now putting this value of P in equation 3H+7P=29.5

we get

3H plus 7 (4.1 minus 0.4H) = 29.5

3H plus 28.7 minus 0.4H=29.5

2.6H = 29.5 minus 28.7

2.6H = 0.8

H = 0.8 divided by 2.6

thus hardcover cost book cost = 0.3077