Question

a student bought 1 box of crayonabd 5 reams of paper for $54. she bought 5 boxes of crayon and 3 reams of paper for $50. what is the cost of each box of crayon and each ream of paper?

Answer 1

let c=cost of crayon and p=cost of paper

c+5p=54
5c+3p=50

Answer 2

how do i solve it

Answer 3

As a system of equations, by substitution or elimination

Answer 4

can you show me

Answer 5

Multiply the first equation by -5, what do you get

Answer 6

why do i mulitply it by -5?

Answer 7

You're going to be adding the two equations together, when you do that you want a variable to be eliminated. c will become -5c and -5c+5c=0

Answer 8

how did it become negative tho?

Answer 9

Because you multiply it by -5...

Answer 10

but dont you have to multipy the 54 by -5 as well?

Answer 11

Yes you multiply the whole equation by -5. so:

-5c-25p=-270
5c+3p=50

now add those equations together

Answer 12

but where did the -5 come from?

Answer 13

We want a variable to be eliminated, so you just think of a number that would make that happen.

Answer 14

so you just make any # up?

Answer 15

Any number that will make it to where when you add the equations together, one of the variables will cancel out.

What do you get when you add them together?