Respuesta :
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.
[tex]2\frac{1}{4}=\frac{9}{4}[/tex]
[tex]1\frac{1}{3}=\frac{4}{3}[/tex]
We can represent this information as:
[tex]\frac{x}{y}=\frac{\frac{9}{4}}{\frac{4}{3}}...(1)[/tex]
We are also told that the supplier sells 172 pounds of mulch and gravel combined. We can represent this information as:
[tex]x+y=172...(2)[/tex]
From equation (1) we will get,
[tex]\frac{x}{y}=\frac{9}{4}*\frac{3}{4}[/tex]
[tex]\frac{x}{y}=\frac{27}{16}[/tex]
[tex]x=y*\frac{27}{16}[/tex]
Substituting this value in equation (2) we will get,
[tex]y*\frac{27}{16}+y=172[/tex]
Now let us have a common denominator.
[tex]\frac{27y}{16}+\frac{16y}{16}=172[/tex]
[tex]\frac{27y+16y}{16}=172[/tex]
[tex]16*\frac{43y}{16}=16*172[/tex]
[tex]43y=2752[/tex]
[tex]y=\frac{2752}{43}[/tex]
[tex]y=64[/tex]
Therefore, the supplier sold 64 pounds of gravel.
Upon substituting y=64 in equation (2) we will get,
[tex]x+64=172[/tex]
[tex]x=172-64[/tex]
[tex]x=108[/tex]
Therefore, the supplier sold 108 pounds of mulch.
