The correct option is d.
Jeremy will need 48 gallons of brown material and 16 gallons of green material.
To solve this problem, we need to first understand the ratio of brown and green materials in the composting container, and then scale it up to meet Jeremy's requirement of 64 gallons of compost.
1. Identify the Ratio:
From the table, we can see that for every set of values, the total amount of compost (brown + green) is given. We can use these to find the ratios.
- For the first set: Brown = 12.75 gallons, Green = 4.25 gallons, Total = 12.75 + 4.25 = 17 gallons
- For the second set: Brown = 18.6 gallons, Green is unknown (let's call it B), Total is unknown (let's call it C)
- For the third set: Brown = 24 gallons, Green is unknown (let's call it D), Total = 32 gallons
2. Calculate the Missing Values:
- We can find the value of B and D by subtracting the amount of brown material from the total for each set.
- For the second set, C (Total) = 18.6 + B
- For the third set, D (Green) = 32 - 24 = 8 gallons
3. Determine the Ratio:
- We can see from the first and third set that the ratio of brown to green material remains consistent. For example, in the first set, the ratio of brown to green is 12.75:4.25. If we simplify this ratio, we get 3:1. This is because 12.75/4.25 = 3.
- The third set also gives a 3:1 ratio, as 24:8 simplifies to 3:1.
4. Scale Up to 64 Gallons:
- Since Jeremy needs 64 gallons of compost, and we know the ratio of brown to green material is 3:1, we can use this ratio to find out how much of each he needs.
- Let's call the amount of brown material Jeremy needs X and green material Y. So, X/Y = 3/1 and X + Y = 64.
- Solving these equations, we get X = 48 gallons (brown material) and Y = 16 gallons (green material).
Therefore, the answer is Jeremy will need 48 gallons of brown material and 16 gallons of green material.