The table below shows the ratio of materials in a composting container.
Brown Material (gallons) 12.75 18.6 24 E
Green Material (gallons) 4.25 B D 11.5
Total (gallons) A C 32 46
If Jeremy needs 48 gallons of compost to plant his garden in the spring, how much brown material will he need? How much green material will he need?
Jeremy will need 36 gallons of brown material and 12 gallons of green material.
Jeremy will need 30 gallons of brown material and 18 gallons of green material.
Jeremy will need 12 gallons of brown material and 36 gallons of green material.
Jeremy will need 15 gallons of brown material and 33 gallons of green material.
To find how much brown material Jeremy needs, we can subtract the total gallons (48) from the sum of the green material (12) and the unknown (brown material):
48 - (12 + B) = 36 - B
To find how much green material Jeremy needs, we can subtract the total gallons (48) from the sum of the brown material (36) and the unknown (green material):
48 - (36 + D) = 12 - D
From the table, we know that the total brown material is 12.75 + 18.6 + 24 + E = A + C + 32 + 46.
Simplifying this equation, we get:
55.35 + E = A + C + 78
Since the total green material is 4.25 + B + D + 11.5 = A + C + 32 + 46, we have:
16.75 + B + D = A + C + 78.
Combining the two equations, we have:
55.35 + E = 16.75 + B + D.
Since all the variables are independent, we cannot determine the exact values of B, D, or E. Therefore, we cannot determine the exact amount of brown or green material that Jeremy will need.
To determine how much brown and green material Jeremy will need, we need to solve the given ratios.
The ratio of brown material to total material is 12.75: A.
The ratio of green material to total material is 4.25: C.
We are given that the total material is 48 gallons (A + C = 48).
Using the given ratios, we can set up the following equations:
12.75/A = 48/C (equation 1)
4.25/C = 12.75/A (equation 2)
To solve these equations, we can set them equal to each other:
12.75/A = 4.25/C
Simplifying this equation, we get:
12.75 * C = 4.25 * A
3 * C = A
Substituting this result into equation 1, we get:
12.75/(3 * C) = 48/C
Again, simplifying and rearranging this equation, we have:
4.25/C = 48/C
This equation implies that C = 48.
Now, we can substitute this value of C into equation 2:
4.25/48 = 12.75/A
Simplifying this equation, we get:
A = 48
So, Jeremy will need 48 gallons of brown material and 48 gallons of green material.
Therefore, none of the given answer choices are correct.