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

Answer:

B

Step-by-step 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:

$p=0.85(p+g)\\(9g-30)=0.85((9g-30)+g)\\9g-30=0.85(10g-30)\\9g-30=8.5g-25.5\\0.5g=-25.5+30\\0.5g=4.5\\g=\frac{4.5}{0.5}\\g=9$

The number of glass items is 9

Answer 2

Answer:

b. 9

Step-by-step explanation:

x : glass items

9x - 30 : plastic items

(the equation will be set equal to $\frac{15}{85}$ because 85% of the recyclables are plastic, so that means 15% must be glass.)

$\frac{x}{9x-30} =\frac{15}{85}$

$85x=135x-450$  (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)

$x=9$