Question

Three reams of recycled paper and five reams of cardstock weigh one hundredpounds. If seven reams of recycled paper weighs as much as five cardstock, howmuch does one ream of each type of paper?

Answer 1

recycled: 10 pounds

cardstock: 14 pounds

Step-by-step explanation:

Let's call x the weight of one ream of recycled paper and y the weight of one ream of cardstock.

If 3 reams of recycled paper and 5 reams of cardstock weigh 100 pounds, we can write the following equation

3x + 5y = 100

Additionally, if 7 reams of recycled paper weigh as much as 5 cardstock, we get

7x = 5y

So, taking into account the last equation, we can replace 5y by 7x in the first equation

3x + 5y = 100

3x + 7x = 100

Then, we can solve for x

10x = 100

10x/10 = 100/10

x = 10

Finally, we can replace x = 10 on 7x = 5y and solve for y as follows

7x = 5y

7(10) = 5y

70 = 5y

70/5 = 5y/5

14 = y

Therefore, the weight of one ream of each type of paper is

recycled: 10 pounds

cardstock: 14 pounds