whats was the specific number of cartons of pencils?

Question

Pencils cost $6 per carton and erasers cost $3 per carton. If an order comes in for a total of 100 cartons for $360, what was the specific number of cartons of pencils? the options are
a: 20
b: 120
c: 80
d: 240
e: none of the above

Answer 1

20

Say
x:= "number of cartons of pencils"
y:="number of cartons of erasers"

Here's what you know:
x + y = 100 (there are 100 cartons overall)
x*6 + y*3 = 360 (the number of each item times their price equals the total price.)

First, we solve the first equation for y (or x, doesn't matter, but I'll use y here:

x + y = 100 | - x
y = 100 - x

Then, we plug that result into our second equation, and solve for x:

x*6 + (100-x)*3 = 360
6x + 300 - 3x = 360 | -300
3x = 60 | :3
x = 20

If you want, you can now also use that result to solve for y:

20 + y = 100 |-20
y = 80

So there are 20 cartons of pencils and 80 of erasers.