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

To find the strength of each sports drink, we need to determine the ratio of powdered mix to water in each drink. The strength of the drink can be defined as the amount of powdered mix per gallon of water.

### Step 1: Calculate the strength of Maria's sports drink
Maria uses \( \frac{2}{3} \) cup of powdered mix for every 2 gallons of water. 

To find the strength (amount of mix per gallon of water):
\[
\text{Strength of Maria's drink} = \frac{\frac{2}{3} \text{ cup}}{2 \text{ gallons}} = \frac{2}{3} \times \frac{1}{2} = \frac{2}{6} = \frac{1}{3} \text{ cup per gallon}
\]

### Step 2: Calculate the strength of Franco's sports drink
Franco uses \( 1 \frac{1}{4} \) cups (which is \( \frac{5}{4} \) cups) of powdered mix for every 5 gallons of water.

To find the strength:
\[
\text{Strength of Franco's drink} = \frac{\frac{5}{4} \text{ cups}}{5 \text{ gallons}} = \frac{5}{4} \times \frac{1}{5} = \frac{5}{20} = \frac{1}{4} \text{ cup per gallon}
\]

### Conclusion:
- **Maria's sports drink strength** is \( \frac{1}{3} \) cup of powdered mix per gallon of water.
- **Franco's sports drink strength** is \( \frac{1}{4} \) cup of powdered mix per gallon of water.

Maria's drink is stronger because \( \frac{1}{3} \) cup per gallon is greater than \( \frac{1}{4} \) cup per gallon.

Would you like more details on any step or have any questions?

### Relative Questions:
1. How would the strength change if Maria used 3 cups of powdered mix for 6 gallons of water?
2. What would happen to Franco’s drink strength if he used 2 cups of mix for 8 gallons of water?
3. How can we compare the strengths if the units of measurement were different (e.g., liters instead of gallons)?
4. What if Maria and Franco mixed their drinks together? How would we calculate the combined strength?
5. How would the strengths compare if both used the same amount of water but different amounts of mix?

### Tip:
When comparing ratios, it’s often helpful to bring both quantities to the same units to make the comparison clearer.

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 calculate and compare the strength of sports drinks by analyzing the ratio of powdered mix to water. This problem is ideal for students in Grades 6-8, covering key concepts like ratios, proportions, and the Proportionality Theorem.

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