Question

Sidney made root beer floats for her friends when they came over. The table shows the ratio of cups of ice cream to cups of soda used to make the floats. Ice Cream (cups) Soda (cups) 3.5 10.5 8 24 12.5 37.5 17 ? At this rate, how much soda will Sidney use for 17 cups of ice cream? 42 cups 51 cups 54 cups 62 cups

Answer 1

To find out how much soda Sidney will use for 17 cups of ice cream, we first need to determine the ratio of ice cream to soda from the given data.

1. First, we will calculate the ratio using the first set of values from the table:

   • For 3.5 cups of ice cream to 10.5 cups of soda, we find the ratio: \[ \frac{\text{Ice Cream}}{\text{Soda}} = \frac{3.5}{10.5} \]
   • Simplifying this gives: \[ \frac{3.5 \div 3.5}{10.5 \div 3.5} = \frac{1}{3} \] Thus, the ratio of ice cream to soda is \(1:3\).

2. Now we can use this ratio to calculate the amount of soda for 17 cups of ice cream. If the ratio of ice cream to soda is \(1:3\), for every 1 cup of ice cream, there are 3 cups of soda.

3. Therefore, for 17 cups of ice cream: \[ \text{Soda} = 17 \text{ cups of ice cream} \times 3 \frac{\text{cups of soda}}{\text{cup of ice cream}} = 51 \text{ cups of soda} \]

So, at this rate, Sidney will use 51 cups of soda for 17 cups of ice cream. The correct answer is 51 cups.