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. What is the strength of each sports

To determine the strength of each sports drink, we calculate the amount of powdered mix per gallon of water for both Maria and Franco. The strength is given as the ratio of powdered mix to the amount 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 (mix per gallon):
\[
\text{Strength of Maria's drink} = \frac{\frac{2}{3} \text{ cup}}{2 \text{ gallons}} = \frac{2}{3} \times \frac{1}{2} = \frac{2}{6} = \frac{1}{3} \text{ cup per gallon}
\]

### 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 (mix per gallon):
\[
\text{Strength of Franco's drink} = \frac{\frac{5}{4} \text{ cups}}{5 \text{ gallons}} = \frac{5}{4} \times \frac{1}{5} = \frac{5}{20} = \frac{1}{4} \text{ cup per gallon}
\]

### 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 slightly stronger because \( \frac{1}{3} \) cup per gallon is more 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 4/3 cups of powdered mix for 4 gallons of water?
2. What would be Franco's drink strength if he used 2 cups of mix for 8 gallons of water?
3. How can the strengths be compared if Maria and Franco used liters instead of gallons?
4. If they mixed their drinks together, how would we calculate the combined strength?
5. What would be

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. What is the strength of each sports drink?

Learn how to calculate the strength of sports drinks by finding the ratio of powdered mix to water. This problem teaches key concepts like fractions, ratios, and unit rate, suitable for students in Grades 5-7.

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