Question

A supplier sells 2 1/4 pounds of mulch for every 1 1/3 pounds of gravel. The supplier sells 1/72 pounds of mulch and gravel combined. How many pounds of each item does the supplier sell?

Answer 1

Answer:

108 pounds of mulch.

64 pounds of gravel.

Step-by-step explanation:

Let x be the amount of mulch sold and y be the amount of gravel sold.

We have been given that a supplier sells 2 1/4 pounds of mulch for every 1 1/3 pounds of gravel.  

$2\frac{1}{4}=\frac{9}{4}$

$1\frac{1}{3}=\frac{4}{3}$

We can represent this information as:

$\frac{x}{y}=\frac{\frac{9}{4}}{\frac{4}{3}}...(1)$

We are also told that the supplier sells 172 pounds of mulch and gravel combined. We can represent this information as:

$x+y=172...(2)$

From equation (1) we will get,

$\frac{x}{y}=\frac{9}{4}*\frac{3}{4}$

$\frac{x}{y}=\frac{27}{16}$

$x=y*\frac{27}{16}$

Substituting this value in equation (2) we will get,

$y*\frac{27}{16}+y=172$

Now let us have a common denominator.

$\frac{27y}{16}+\frac{16y}{16}=172$

$\frac{27y+16y}{16}=172$

$16*\frac{43y}{16}=16*172$

$43y=2752$

$y=\frac{2752}{43}$

$y=64$  

Therefore, the supplier sold 64 pounds of gravel.

Upon substituting y=64 in equation (2) we will get,

$x+64=172$

$x=172-64$

$x=108$

Therefore, the supplier sold 108 pounds of mulch.