Question

A store sells 2 1/4 pounds of mulch for every 1 1/2 pounds of gravel sold. The store sells 180 pounds of mulch and gravel combined. How many pounds of each item does the store sell?

Answer 1

The pounds of mulch the store sells are 108 and the pounds of gravel the store sells are 72.

Explanation:

Let

x -----> pounds of mulch the store sells

y ----> pounds of gravel the store sells

we know that

`x+y=180` -----> equation A

Remember that

`2(1)/(4)\ lb=(2*4+1)/(4)=(9)/(4)\ lb`

`1(1)/(2)\ lb=(1*2+1)/(2)=(3)/(2)\ lb`

so

`(x)/(y)=((9/4))/((3/2))`

`(x)/(y)=(3)/(2)`

`x=(3)/(2)y` -----> equation B

solve the system by substitution

substitute equation B in equation A

`(3)/(2)y+y=180`

solve for y

`(5)/(2)y=180`

`y=180(2)/5\\y=72`

Find the value of x

`x=(3)/(2)(72)=108`

The solution is the ordered pair (108,72)

therefore

The pounds of mulch the store sells are 108 and the pounds of gravel the store sells are 72.