I'm in algebra 1 and i need on this 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?

The cost of a hardcover book is $4

Step-by-step explanation:

Let the cost of one hard cover book be $x

Let the cost of one paper back book be $y

Nate bought 3 hardcover books and 7 paperback books and spent $29.50. This means that

3x + 7y = 29.5 - - - - - - - - - 1

Tia bought 2 hardcover books and 5 paperback books and spent $20.50. This means that

2x + 5y = 20.5 - - - - - - - - -2

Multiplying equation 1 by 2 and equation 2 by 3. It becomes

6x + 14y = 59

6x + 15y = 61.5

Subtracting,

- y = - 2.5

y = 2.5

Substituting y = 2.5 into equation 1, it becomes

3x + 7×2.5 = 29.5

3x + 17.5 = 29.5

3x = 29.5 - 17.5 = 12

x = 12/3 = 4