Final answer:
To make 1 gallon of iced tea, 5/6 cup of sugar is needed, based on the recipe proportion that calls for 2/3 cup sugar for 4/5 gallon of tea.
Step-by-step explanation:
The student is asking how much sugar is needed to make 1 gallon of iced tea if the recipe calls for 2/3 cup sugar to make 4/5 gallon of iced tea. To find the answer, we need to set up a proportion that compares the amount of sugar to the amount of iced tea. The proportion will be (2/3) cups sugar / (4/5) gallon iced tea = x cups sugar / 1 gallon iced tea.
To solve for x, cross-multiply and divide as follows:
(2/3) × 1 = x × (4/5)
→ x = (2/3) × (5/4)
→ x = (2 × 5) / (3 × 4)
→ x = 10/12
→ x = 5/6
So, 5/6 cup of sugar is needed to make 1 gallon of iced tea.