Final answer:
To make a 16-cup mixture with a ratio of 1 part lemonade to 1.5 parts iced tea, you need 6.4 cups of lemonade and 9.6 cups of iced tea.
Step-by-step explanation:
The student's question involves determining the amount of lemonade and iced tea needed to create a mixture in a specific ratio. The total amount of the mixture that needs to be made is given as 16 cups. The recipe specifies a ratio of 1 part lemonade to 1.5 parts iced tea. To solve this, we must set up the proportions such that the sum of lemonade and iced tea equals 16 cups.
Set up the proportion for lemonade (L) and iced tea (T) as follows:
- L + T = 16 cups (total mixture)
- L / T = 1 / 1.5 (ratio of lemonade to iced tea)
From the ratio, we can express lemonade in terms of iced tea: L = (1/1.5) * T
Substitute L in the total mixture equation:
- (1/1.5) * T + T = 16 cups
- (1 + 1.5)/1.5 * T = 16 cups
- 2.5/1.5 * T = 16 cups
- T = (1.5/2.5) * 16 cups
- T = 0.6 * 16 cups
- T = 9.6 cups of iced tea
Now, we can find the amount of lemonade:
- L = 16 cups - T
- L = 16 cups - 9.6 cups
- L = 6.4 cups of lemonade
Therefore, for a 16-cup mixture based on the recipe, one would need 6.4 cups of lemonade and 9.6 cups of iced tea.