Find the cost of a pencil and eraser if two pencils and three erasers cost 140 dollars, and fivepencils and four erasers cost 280 dollars.

Guest Mar 16, 2021

#1**0 **

let's define a variable *p *for pencils and *e *for erasers.

now we can set up a sysem of equations.

2p + 3e = 140

and

5p + 4e = 280

for this problem, i'm going to use elimination.

we multiplfy the first equation by 5 and the second equation by 2.

10p + 15e = 700

10p + 8e = 560

notice how we now have a 10p on both equations. we can subtract the two equations to cancel those out.

7e = 700 - 560

7e = 140

**e = 20**

now we can solve for p.

2p + 3(20) = 140

2p + 60 = 140

2p = 80

**p = 40**

hope this helped! please let me know if you are confused about anything i did

euph0ria Mar 16, 2021