https://file.aiquickdraw.com/mathbot/file/1726082880529rs6ktkgs.jpg

The question in the image reads:

**"An engine runs on a mixture of 0.1 quarts of oil for every 3.5 quarts of gasoline. You make 3 quarts of the mixture. How much oil and how much gasoline do you use?"**

### Solution:
Let’s break it down step by step.

1. **Total mixture**: You are making 3 quarts of the mixture.
2. **Ratio of oil to gasoline**: 0.1 quarts of oil for every 3.5 quarts of gasoline. This means the ratio of oil to the total mixture is:
   \[
   \frac{0.1}{0.1 + 3.5} = \frac{0.1}{3.6}
   \]
   Similarly, the ratio of gasoline to the total mixture is:
   \[
   \frac{3.5}{3.6}
   \]
3. **Finding the amount of oil**:
   Multiply the total mixture (3 quarts) by the fraction of oil in the mixture:
   \[
   \text{Oil used} = 3 \times \frac{0.1}{3.6} = \frac{0.3}{3.6} = 0.0833 \text{ quarts of oil}
   \]
4. **Finding the amount of gasoline**:
   Multiply the total mixture (3 quarts) by the fraction of gasoline:
   \[
   \text{Gasoline used} = 3 \times \frac{3.5}{3.6} = \frac{10.5}{3.6} = 2.9167 \text{ quarts of gasoline}
   \]

### Final Answer:
- **Oil used**: 0.0833 quarts
- **Gasoline used**: 2.9167 quarts

Would you like a more detailed explanation or have any further questions?

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Here are 5 related questions you might find helpful:
1. How would the mixture change if you needed 5 quarts of the total mixture?
2. If the ratio of oil to gasoline changes, how would you adjust the calculations?
3. How many quarts of gasoline would you need if you doubled the amount of oil?
4. Can you express the ratio of oil to gasoline in a simplified form?
5. What happens to the amount of oil used if you increase the total mixture to 10 quarts?

**Tip**: When working with ratios, always keep in mind that the total amount must respect the ratio’s relationship across different parts (oil and gasoline in this case).

An engine runs on a mixture of 0.1 quarts of oil for every 3.5 quarts of gasoline. You make 3 quarts of the mixture. How much oil and how much gasoline do you use?

Learn how to solve a mixture problem where an engine uses 0.1 quarts of oil for every 3.5 quarts of gasoline. In this case, the total mixture is 3 quarts. Find the exact amount of oil and gasoline needed using ratios and basic arithmetic.

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