Question

The recyclables have been sorted into plastic and glass. The number of plastic items is 30 less than nine times the number of glass items. The recyclables are 85% plastic. How many glass items are there?

a. 6
b. 9
c. 15
d. 18

Answer 1

b. 9

Explanation:

x : glass items

9x - 30 : plastic items

(the equation will be set equal to
`(15)/(85)` because 85% of the recyclables are plastic, so that means 15% must be glass.)

`(x)/(9x-30) =(15)/(85)`

`85x=135x-450` (now subtract 135x from each side to isolate x to one side of the equation)

`-50x=-450` (divide each side of the equation by -50 to isolate x)

`x=9`

Answer 2

B

Explanation:

We will use substitution method after writing 2 equations to solve for number of glass items.

Let number of glass items be g and number of plastic items be p

"The number of plastic items is 30 less than nine times the number of glass items":

We can write the equation as
`p=9g-30`

"The recyclables are 85% plastic":

This means that plastic (p) is 0.85 of the total (p+g). Thus we can write equation as
`p=0.85(p+g)`

We can substitute the expression for p in first equation into 2nd and solve for g:

`p=0.85(p+g)\\(9g-30)=0.85((9g-30)+g)\\9g-30=0.85(10g-30)\\9g-30=8.5g-25.5\\0.5g=-25.5+30\\0.5g=4.5\\g=(4.5)/(0.5)\\g=9`

The number of glass items is 9