https://file.aiquickdraw.com/mathbot/file/172626067412462mucyad.jpg

The problem in the image involves finding the strength of two sports drinks made by Maria and Franco. Let's break this down:

**Maria's Mixture:**
- Maria uses \( \frac{2}{3} \) cup of mix for every 2 gallons of water.
- To find the amount of mix per gallon, divide \( \frac{2}{3} \) by 2 (since it's for 2 gallons):
  \[
  \text{Mix per gallon for Maria} = \frac{\frac{2}{3}}{2} = \frac{2}{3} \times \frac{1}{2} = \frac{2}{6} = \frac{1}{3} \text{ cup(s) per gallon}.
  \]

**Franco's Mixture:**
- Franco uses \( 1 \frac{1}{4} \) cups (which is \( \frac{5}{4} \)) of mix for 5 gallons of water.
- To find the amount of mix per gallon, divide \( \frac{5}{4} \) by 5:
  \[
  \text{Mix per gallon for Franco} = \frac{\frac{5}{4}}{5} = \frac{5}{4} \times \frac{1}{5} = \frac{5}{20} = \frac{1}{4} \text{ cup(s) per gallon}.
  \]

Thus, the strength of each sports drink is:
- **Maria**: \( \frac{1}{3} \) cups per gallon.
- **Franco**: \( \frac{1}{4} \) cups per gallon.

If you need further clarification or additional steps, feel free to ask!

### Expanding Questions:
1. How would you calculate the total amount of mix needed if Maria made 10 gallons of her drink?
2. How would you compare the strengths of Maria's and Franco's mixtures?
3. If Franco wanted to make a stronger mix than Maria's, what could he do?
4. How does the ratio of water to mix affect the taste of the sports drink?
5. What is the mathematical process for converting mixed numbers like \( 1 \frac{1}{4} \) to improper fractions?

### Tip:
Always ensure that your units match (cups per gallon, etc.) when working with ratios or proportions to avoid calculation errors.

Maria and Franco are mixing sports drinks for a track meet. Maria uses 2/3 cup of powdered mix for every 2 gallons of water. Franco uses 1 1/4 cups of powdered mix for every 5 gallons of water. Show how you can find the strength of each sports drink.

Learn how to find the strength of sports drinks by calculating the mix per gallon for Maria and Franco using ratios and division of fractions. Suitable for students in Grades 5-6.

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