Question

A supplier sells 2 1/4 pounds of mulch for every 1 1/3 pounds of gravel. The supplier sells 173 pounds of mulch and gravel combined. How many pounds of each item does the supplier sell?

Answer 1

Divide 11 by 3 21 by 4 by 173

Answer 2

`(4,671)/(59) pounds` of mulch and
`(5,536)/(59)pounds` of gravel were sold.

Explanation:

Mass of mulch sold = x pounds

Mass of gravel sold = y pounds

Total mass of mulch and gravel sold = 173 pounds

x + y = 173 ...[1]

Supplier sells
`2(1)/(4)` pounds of mulch for every
`1(1)/(3)` pounds of gravel.

That is for
`(9)/(8)` pounds of mulch for every
`(4)/(3)` pounds of gravel.

Then gravel sold for 1 pound mulch =
`(4)/(3)* (8)/(9)=(32)/(27) pounds`

Then for x pounds of mulch the gravel sold will be:

`(32)/(27) pounds* x`

Mass of gravel sold =
`y = (32)/(27) pounds* x`

Putting value of y in [1] :

`x + (32)/(27) pounds* x = 173`

x =
`(4,671)/(59) pounds`

y =
`173 pounds -(4,671)/(59) pounds=(5,536)/(59)pounds`

`(4,671)/(59) pounds` of mulch and
`(5,536)/(59)pounds` of gravel were sold.