A supplier sellers 2 1/4 pounds of mulch for every 1 1/3 pounds of gravel. The supplier sells 172 pounds of mulch and gravel combined. How many pounds of each item does the supplier sell?
To solve this problem, we can set up a system of equations. Let's consider the pounds of mulch as M and the pounds of gravel as G.
According to the problem statement, the supplier sells 2 1/4 (or 2.25) pounds of mulch for every 1 1/3 (or 1.333) pounds of gravel. Therefore, we can write the equation:
M = 2.25G (Equation 1)
The supplier sells a total of 172 pounds of mulch and gravel combined. So we can also write another equation:
M + G = 172 (Equation 2)
Now, we have a system of equations to solve. We can use substitution or elimination method to find the values of M and G.
Let's use substitution method. From equation 1, we can express M in terms of G:
M = 2.25G
Substitute this value of M into equation 2:
2.25G + G = 172
Combine like terms:
3.25G = 172
Divide both sides of the equation by 3.25:
G = 172 / 3.25
G ≈ 53.23
Since it doesn't make sense to have a fraction of a pound, we can round G to the nearest whole number:
G ≈ 53
Now, substitute this value of G into equation 1 to find M:
M = 2.25 * 53
M ≈ 119.25
Again, rounding M to the nearest whole number, we get:
M ≈ 119
Therefore, the supplier sells approximately 119 pounds of mulch and 53 pounds of gravel.
If there are x lbs of mulch, then the rest (172-x) is gravel.
So,
2 1/4 * x + 1 1/3 (172-x) = 172
Now just find x