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

Answer:

$\frac{4,671}{59} pounds$ of mulch and $\frac{5,536}{59}pounds$ of gravel were sold.

Step-by-step 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 $2\frac{1}{4}$ pounds of mulch for every $1\frac{1}{3}$ pounds of gravel.

That is for $\frac{9}{8}$ pounds of mulch for every $\frac{4}{3}$ pounds of gravel.

Then gravel sold for 1 pound mulch = $\frac{4}{3}\times \frac{8}{9}=\frac{32}{27} pounds$

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

$\frac{32}{27} pounds\times x$

Mass of gravel sold = $y = \frac{32}{27} pounds\times x$

Putting value of y in [1] :

$x + \frac{32}{27} pounds\times x = 173$

x =$\frac{4,671}{59} pounds$

y = $173 pounds -\frac{4,671}{59} pounds=\frac{5,536}{59}pounds$

$\frac{4,671}{59} pounds$ of mulch and $\frac{5,536}{59}pounds$ of gravel were sold.