Recipe needs to make exactly 10 cups. 5 ingredients. Using 1/3 cups and/or 1/4 cups only. Please help.
To make exactly 10 cups using 1/3 cups and/or 1/4 cups, you can follow these steps:
1. Determine the combination of 1/3 cups and 1/4 cups needed to make a whole number of cups (e.g., 1, 2, 3, etc.). Since both 1/3 and 1/4 cups are factors of 1 (the least common multiple), you can create combinations by simply incrementing the number of 1/4 cups used while decreasing the number of 1/3 cups.
2. Start with a base combination of 3/4 cups (2/3 cup + 1/6 cup) and calculate the number of cups it yields. You can do this by finding a common denominator (6), adding the numerators (4 + 1), and dividing the sum by the denominator (5/6).
3. Multiply the base combination by a factor to obtain multiple cups. Since the base combination yields 5/6 cups, you need to find a factor that results in 10 cups. In this case, the factor is 10 divided by 5/6, which is 12/5 (or 2 2/5).
4. Multiply each component of the base combination by the factor to get the final recipe:
- 2/3 cup * 2 2/5 = 10/5 cups = 2 cups
- 1/6 cup * 2 2/5 = 5/5 cups = 1 cup
The final recipe to make exactly 10 cups using 1/3 cups and/or 1/4 cups is 2 cups of the 2/3 cup ingredient and 1 cup of the 1/6 cup ingredient.