Question

Javier is making a special fertilizer for his garden. The ingredients are mixed in the ratios shown below. • 3} 8of the fertilizer is cottonseed. • 1} 4of the fertilizer is phosphate. • 1} 4of the fertilizer is wood ash. • 1} 8of the fertilizer is limestone. Part A Javier makes 24 cups of fertilizer every week. How many cups of each ingredient does he use each week? Enter your answers and your work in the box provided.

Answer 1

To find out how many cups of each ingredient Javier uses to make 24 cups of fertilizer, we can calculate the amount of each ingredient based on the ratios provided.

The total ratio of the ingredients must equal 1 (or \( \frac{8}{8} \)). Let's first convert the ratios into a common denominator:

- Cottonseed: \( \frac{3}{8} \)
- Phosphate: \( \frac{1}{4} = \frac{2}{8} \)
- Wood ash: \( \frac{1}{4} = \frac{2}{8} \)
- Limestone: \( \frac{1}{8} \)

Now, summing these fractions:

\[
\frac{3}{8} + \frac{2}{8} + \frac{2}{8} + \frac{1}{8} = \frac{3 + 2 + 2 + 1}{8} = \frac{8}{8} = 1
\]

Now we can calculate the amount of each ingredient in 24 cups of fertilizer:

1. **Cottonseed:**
\[
\text{Cottonseed} = \frac{3}{8} \times 24 = 9 \text{ cups}
\]

2. **Phosphate:**
\[
\text{Phosphate} = \frac{1}{4} \times 24 = \frac{2}{8} \times 24 = 6 \text{ cups}
\]

3. **Wood Ash:**
\[
\text{Wood Ash} = \frac{1}{4} \times 24 = \frac{2}{8} \times 24 = 6 \text{ cups}
\]

4. **Limestone:**
\[
\text{Limestone} = \frac{1}{8} \times 24 = 3 \text{ cups}
\]

Putting it all together, Javier uses the following amounts of each ingredient each week:

- Cottonseed: **9 cups**
- Phosphate: **6 cups**
- Wood Ash: **6 cups**
- Limestone: **3 cups**

Thus, the final amounts are:

- **Cottonseed:** 9 cups
- **Phosphate:** 6 cups
- **Wood Ash:** 6 cups
- **Limestone:** 3 cups