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The question in the image is asking how many grams of a 70% clay mix must be combined with 15 grams of a 30% clay mix to obtain a final mixture that is 50% clay.

To solve this, we need to set up an equation based on the percentage concentrations and amounts of clay in each mixture.

Let's define:
- \( x \) = grams of 70% clay mix to be added.

We know:
- The 30% clay mix has 15 grams, so the amount of clay in this mix is \( 0.30 \times 15 = 4.5 \) grams.
- The 70% clay mix has \( x \) grams, so the amount of clay in this mix is \( 0.70x \).

The total amount of clay in the final mixture will be \( 4.5 + 0.70x \) grams.
The total weight of the final mixture is \( 15 + x \) grams.

We want this final mixture to be 50% clay, so we set up the equation:

\[
\frac{4.5 + 0.70x}{15 + x} = 0.50
\]

Now, solve for \( x \):

1. Multiply both sides by \( 15 + x \):

\[
4.5 + 0.70x = 0.50(15 + x)
\]

2. Expand and simplify:

\[
4.5 + 0.70x = 7.5 + 0.50x
\]

3. Subtract \( 0.50x \) from both sides:

\[
4.5 + 0.20x = 7.5
\]

4. Subtract 4.5 from both sides:

\[
0.20x = 3
\]

5. Divide by 0.20:

\[
x = \frac{3}{0.20} = 15
\]

So, you need to add **15 grams** of the 70% clay mix.

### Answer:
**15 grams** of the 70% clay mix must be added to 15 grams of the 30% clay mix to obtain the required 50% clay mixture.

Would you like more details or have any questions?

### Related Questions:
1. How would the mixture change if 10 grams of 30% clay is used instead of 15 grams?
2. What is the final weight of the mixture if 20 grams of 70% clay is used?
3. How do you set up a similar mixture problem with different percentages?
4. What happens to the percentage of clay if you mix equal parts of a 70% and 50% clay mixture?
5. Can this type of problem be solved using a system of equations?

### Tip:
For mixture problems involving percentages, always set up equations based on the total amount and the desired concentration to find the correct proportions.

A chemist needs a 50% clay mix. How many grams of a 70% clay mix must be mixed with 15 grams of a 30% clay mix to obtain the required 50% clay?

Learn how to solve a mixture problem by determining how many grams of a 70% clay mix must be added to 15 grams of a 30% clay mix to achieve a 50% clay mixture. This step-by-step guide is perfect for students in Grades 9-10.

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