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?

PLEASE HELP ASAP

Answer 1

B, 9

Explanation:

Let g represent the number of glass items. Then the number of plastic items is (9g -30). If 85% of items are plastic, then 100%-85% = 15% of items are glass. The ratio of plastic to glass is ...

85%/15% = (9g -30)/g

17/3 = 9 -30/g . . . . simplify

30/g = 9 -17/3 = 10/3 . . . . . . add 30/g -17/3

g = 30(3/10) = 9 . . . . . . . . . . multiply by 3g/10

There are 9 glass items.

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Additional comment

The number of plastic items is 9(9) -30 = 51, and the total number of items is 51+9 = 60. The percentage of plastic items is 51/60 = 85%.

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There are many other ways the equation(s) could be written, including using a system of two equations. For example ...

• p = 9g -30
• p/(p+g) = 0.85 . . . . . plastic is 85% of the total