Mixture ratio diagram illustrating supplement and grain components with percentage and part values.

It looks like you've uploaded a diagram related to a mixture problem, specifically involving alligation (a method used in chemistry and pharmacy to find the ratio in which two or more ingredients at different concentrations must be mixed to produce a mixture of desired concentration).

Let’s analyze the image and solve the problem step by step.

---

🔍 Diagram Interpretation:

The diagram shows a cross (or alligation) method with four values:

- Top left: 47.0 → This is likely the concentration of one ingredient (e.g., supplement mixture).
- Bottom left: 10.0 → Concentration of the other ingredient (grain mixture).
- Right side:
- Top: 5.0 parts
- Bottom: 32.0 parts
- Center: 15% → The desired concentration of the final mixture.

We are to determine how much of each mixture (supplement and grain) should be combined to get a 15% mixture, using the alligation method.

---

✔ Alligation Method Overview:

Alligation is used to find the ratio of two ingredients with different concentrations to achieve a desired concentration.

The formula for alligation is:

$$
\text{Ratio} = \frac{\text{Higher concentration} - \text{Desired}}{\text{Desired} - \text{Lower concentration}}
$$

But in this case, the diagram already gives us the parts:

- Supplement mixture: 5.0 parts
- Grain mixture: 32.0 parts

And we can see that:

- Supplement mixture has 47.0% (likely)
- Grain mixture has 10.0%
- Desired mixture: 15%

Let’s verify if the parts make sense.

---

🧮 Step-by-step Verification:

We use the alligation cross:

```
47.0% (Supplement)
\
\ 15%
\ /
X
/ \
/ \
10.0% (Grain)
```

Now compute the differences:

- Difference between 47.0 and 15:
$ 47.0 - 15 = 32.0 $
- Difference between 15 and 10.0:
$ 15 - 10.0 = 5.0 $

So, the ratio of supplement : grain is:

$$
\text{Supplement} : \text{Grain} = 5.0 : 32.0
$$

Wait — this seems reversed!

In alligation, the difference from higher to desired goes to the lower concentration, and vice versa.

Let’s clarify:

- Supplement: 47.0% → too high
- Grain: 10.0% → too low
- Desired: 15%

So:

- Amount of grain needed (to dilute): $ 47.0 - 15 = 32.0 $
- Amount of supplement needed: $ 15 - 10.0 = 5.0 $

So the ratio of supplement : grain is:

$$
\text{Supplement} : \text{Grain} = 5.0 : 32.0
$$

This matches what’s shown on the right side of the diagram.

> But wait — in the diagram, 5.0 parts is next to 47.0, and 32.0 parts is next to 10.0.

That means:

- 5.0 parts of supplement mixture (47.0%)
- 32.0 parts of grain mixture (10.0%)

Yes — this makes sense.

---

✔ Final Answer:

To make a 15% mixture:

- Mix 5.0 parts of supplement mixture (47.0%)
- With 32.0 parts of grain mixture (10.0%)

The total parts = $ 5 + 32 = 37 $ parts

So the ratio is:

$$
\boxed{5 : 32}
$$

Or as a fraction:

- Supplement: $ \frac{5}{37} $ of the total
- Grain: $ \frac{32}{37} $ of the total

---

✔ Verification:

Check the weighted average:

$$
\text{Final concentration} = \frac{(5 \times 47.0) + (32 \times 10.0)}{37} = \frac{235 + 320}{37} = \frac{555}{37} = 15.0\%
$$

✔ Confirmed!

---

📌 Conclusion:

The diagram correctly shows an alligation calculation to mix:

- 5.0 parts of 47.0% supplement mixture
- 32.0 parts of 10.0% grain mixture

to obtain a 15% mixture.

✔ Answer: The correct mixing ratio is 5 parts supplement to 32 parts grain.