To solve this problem, let's analyze the information given:

1. Timmy uses $1 \frac{1}{2}$ cups of sugar for every 2 gallons of lemonade.
2. We need to find how many cups of sugar he would use for 13 gallons of lemonade.

Step-by-Step Solution:

1. Convert $1 \frac{1}{2}$ cups to an improper fraction: $1 \frac{1}{2} = \frac{3}{2} \text{ cups}$

2. Set up the proportion based on the information:

   • Timmy uses $\frac{3}{2}$ cups for every 2 gallons.
   • We want to find the amount of sugar for 13 gallons.

   Let $x$ represent the number of cups of sugar needed for 13 gallons. Then we have the proportion: $\frac{3}{2} \text{ cups} : 2 \text{ gallons} = x \text{ cups} : 13 \text{ gallons}$

3. Set up the equation from the proportion: $\frac{3}{2} \times 13 = 2 \times x$

4. Solve for $x$: $\frac{39}{2} = 2x$ $x = \frac{39}{4} = 9.75$

Therefore, Timmy would use 9.75 cups of sugar for 13 gallons of lemonade.

Would you like further clarification, or do you have any questions about this solution?

Related Questions:

1. How much sugar would Timmy need if he made 20 gallons of lemonade?
2. If Timmy has 15 cups of sugar, how many gallons of lemonade can he make?
3. What is the unit rate of sugar per gallon for Timmy's lemonade recipe?
4. How many cups of sugar would Timmy need for 1 gallon of lemonade?
5. If Timmy uses only 1 cup of sugar per 2 gallons, how would that affect the amount needed for 13 gallons?

Tip:

When dealing with mixed numbers, it's often easier to convert them into improper fractions for calculations.