Answer:
[tex]\frac{4,671}{59} pounds[/tex] of mulch and [tex]\frac{5,536}{59}pounds[/tex] 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 [tex]2\frac{1}{4}[/tex] pounds of mulch for every [tex]1\frac{1}{3}[/tex] pounds of gravel.
That is for [tex]\frac{9}{8}[/tex] pounds of mulch for every [tex]\frac{4}{3}[/tex] pounds of gravel.
Then gravel sold for 1 pound mulch = [tex]\frac{4}{3}\times \frac{8}{9}=\frac{32}{27} pounds[/tex]
Then for x pounds of mulch the gravel sold will be:
[tex]\frac{32}{27} pounds\times x[/tex]
Mass of gravel sold = [tex]y = \frac{32}{27} pounds\times x[/tex]
Putting value of y in [1] :
[tex]x + \frac{32}{27} pounds\times x = 173[/tex]
x =[tex]\frac{4,671}{59} pounds[/tex]
y = [tex]173 pounds -\frac{4,671}{59} pounds=\frac{5,536}{59}pounds[/tex]
[tex]\frac{4,671}{59} pounds[/tex] of mulch and [tex]\frac{5,536}{59}pounds[/tex] of gravel were sold.
