https://file.aiquickdraw.com/mathbot/file/1729565538999acs8fqz9.jpg

I see the image you’ve uploaded, and it contains several math problems from a textbook. I will solve problem 17 for you, which is a mixture problem:

**Problem 17:**
Kim sells Pistachio Pleasure, containing 80% pistachio nuts, and Pistachio Surprise, containing 30% pistachio nuts. How much of each should she mix to make 12 lb of a new mix that is 40% pistachio nuts?

### Solution:
Let:
- \( x \) be the amount (in pounds) of Pistachio Pleasure (80% pistachios) to mix.
- \( 12 - x \) be the amount (in pounds) of Pistachio Surprise (30% pistachios) to mix.

We set up the equation based on the amount of pistachios in the mixture:

\[
0.80x + 0.30(12 - x) = 0.40 \times 12
\]

1. Simplify the equation:

\[
0.80x + 0.30(12 - x) = 4.8
\]
\[
0.80x + 3.6 - 0.30x = 4.8
\]

2. Combine like terms:

\[
0.50x + 3.6 = 4.8
\]

3. Subtract 3.6 from both sides:

\[
0.50x = 1.2
\]

4. Solve for \( x \):

\[
x = \frac{1.2}{0.50} = 2.4
\]

So, Kim should mix **2.4 lb of Pistachio Pleasure** and:

\[
12 - 2.4 = 9.6 \, \text{lb of Pistachio Surprise}.
\]

### Final Answer:
- **2.4 lb of Pistachio Pleasure (80%)**
- **9.6 lb of Pistachio Surprise (30%)**

Would you like further details or explanation on this problem?

Here are five related questions you might want to explore:
1. What if the desired mixture were 50% pistachio nuts instead of 40%?
2. How would the equation change if the total weight of the mixture were 20 lb instead of 12 lb?
3. What if one type of pistachio mix was unavailable—how could you adjust the equation?
4. Could you use graphical methods to solve mixture problems like this one?
5. How can you check if the final mixture contains exactly 40% pistachios?

**Tip:** For mixture problems, always keep track of the total quantity and the percentage of the desired component to set up your equation.

Kim sells Pistachio Pleasure, containing 80% pistachio nuts, and Pistachio Surprise, containing 30% pistachio nuts. How much of each should she mix to make 12 lb of a new mix that is 40% pistachio nuts?

Learn how to solve a mixture problem involving pistachio percentages. Kim sells two types of nut mixtures, and we determine how much of each to mix to get 12 pounds of a 40% pistachio mixture. This solution uses algebraic methods, specifically a linear equation, and is ideal for students in Grades 7-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation