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
15 ?
At this rate, how much soda will Sidney use for 15 cups of ice cream?
30 cups
35 cups
40 cups
45 cups
To find the amount of soda that Sidney will use for 15 cups of ice cream, we need to use the given ratio of cups of ice cream to cups of soda.
The ratio is:
3.5 cups of ice cream : 10.5 cups of soda
8 cups of ice cream : 24 cups of soda
12.5 cups of ice cream : 37.5 cups of soda
From this, we can see that the ratio is consistent: for every 3.5 cups of ice cream, there are 10.5 cups of soda.
To find the amount of soda for 15 cups of ice cream, we can set up a proportion:
3.5 cups of ice cream / 10.5 cups of soda = 15 cups of ice cream / x cups of soda
Cross-multiplying, we get:
3.5 cups of ice cream * x cups of soda = 10.5 cups of soda * 15 cups of ice cream
Simplifying, we have:
3.5x = 157.5
Dividing both sides by 3.5, we get:
x = 45
Therefore, Sidney will use 45 cups of soda for 15 cups of ice cream.
To find out how much soda Sidney will use for 15 cups of ice cream, we need to find the ratio of cups of ice cream to cups of soda and then use that ratio to calculate the amount of soda needed.
First, let's calculate the ratio of cups of ice cream to cups of soda by dividing the number of cups of ice cream by the number of cups of soda for each given pair:
Ratio = Cups of Ice Cream / Cups of Soda
For the first pair, the ratio is 3.5 / 10.5 = 1/3.
For the second pair, the ratio is 8 / 24 = 1/3.
For the third pair, the ratio is 12.5 / 37.5 = 1/3.
From this, we can see that the ratio remains consistent at 1/3.
Now, we can use this ratio to calculate the amount of soda needed for 15 cups of ice cream:
Amount of Soda for 15 cups of ice cream = Ratio * Cups of Ice Cream
= (1/3) * 15
= 5 cups
Therefore, Sidney will use 5 cups of soda for 15 cups of ice cream.
The correct answer is 5 cups.