Middle School

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A supplier sells \(2 \frac{1}{4}\) lbs of mulch for every \(1 \frac{1}{3}\) lbs of gravel. The supplier sells 172 pounds of them combined. How many pounds of each does the supplier sell?

Answer :

Answer:

  • 108 lb mulch
  • 64 lb gravel

Step-by-step explanation:

Given a supplier sells 2 1/4 lbs mulch for every 1 1/3 lbs gravel, you want to know the weight of each if 172 total pounds were sold.

Ratio

The ratio of pounds sold can be found as ...

mulch : gravel = 2 1/4 : 1 1/3 = 9/4 : 4/3 = 27/12 : 16/12 = 27 : 16

Fraction

The fraction of mulch sold is 27/(27+16) = 27/43. In pounds, that fraction is ...

(172 lb)(27/43) = 108 lb . . . . . mulch

The rest is sold as gravel:

172 lb -108 lb = 64 lb . . . . . gravel

The supplier sold 108 lb of mulch and 64 lb of gravel.

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