David uses 1/3 cup of apple juice for every 1/2 cup of cranberry juice to make a fruit drink.
What is your question?
To find out how much apple juice David will use if he wants to make a fruit drink with a certain amount of cranberry juice, you'll need to follow these steps:
1. Determine the ratio between apple juice and cranberry juice: David uses 1/3 cup of apple juice for every 1/2 cup of cranberry juice. This means that the ratio of apple juice to cranberry juice is 1/3:1/2.
2. Simplify the ratio: To simplify the ratio, you can multiply both parts of the ratio by the same number to get equivalent fractions. In this case, you can multiply both parts by 6 to eliminate the fractions. This gives you a simplified ratio of 2:3.
3. Calculate the amount of apple juice: If David wants to make a fruit drink with a certain amount of cranberry juice, you can use the ratio to determine how much apple juice he needs. For example, if David wants to use 1 cup of cranberry juice, you can set up a ratio proportion:
2 cups of apple juice / 3 cups of cranberry juice = X cups of apple juice / 1 cup of cranberry juice
Solving for X, the amount of apple juice needed, you can cross-multiply:
(2 cups of apple juice) * (1 cup of cranberry juice) = (3 cups of cranberry juice) * (X cups of apple juice)
Simplifying the equation:
2 / 3 = X / 1
Cross-multiplying again:
(2 cups of apple juice) * (1) = (3 cups of cranberry juice) * (X cups of apple juice)
2 = 3X
Finally, divide both sides of the equation by 3:
X = 2 / 3
So, if David wants to make a fruit drink with 1 cup of cranberry juice, he would need approximately 2/3 cup of apple juice.