Question

Dylan loves reading. He went to buy books from a bookstore. A school bag and 3 books cost $180. A school bag and 5 books cost $270. How much did each book cost?

Answer 1

Each book costed 45$.

Explanation:

Let x represent the price of a school bag and y represent the price of a book.

we get the following system of equations:

x+3y=180 (equation 1)

x+5y=270 (equation 2)

using equation 1: x=180-3y

then we substitute x in equation 2 in order to find y:

180-3y+5y=270

180+2y=270

2y=270-180=90

y=90/2=45

and we know that y represents the price of a book, so each book costs 45$.

Answer 2

School bag _ y

book _ x

system:

y+3x=180

y+5x=270

y=180-3x (and we put that instead of 'y' in the second equation)

(180-3x)+5x=270

180+2x=270

2x=90

x=45

so one book costs $45

and school bag:

y+3×45=180

y+135=180

y=180-135

y=45