Question

you need 4 cups of orange juice and 3 cups of cranberry juice to make 7 total cups of fruit punch. how many cups of each juice do you need for 28 cups of fruit punch? how many total cups of fruit punch do you need to make? orange juice (cups) 4 boxes cranberry juice (cups) 3 boxes total box

Explanation:

Part 1: Cups of each juice for 28 cups of punch

Step1: Find the scaling factor

The original total is 7 cups, and we need 28 cups. The scaling factor \( k \) is \( \frac{28}{7}=4 \).

Step2: Calculate orange juice

Original orange juice is 4 cups. Scaled orange juice: \( 4\times4 = 16 \) cups.

Step3: Calculate cranberry juice

Original cranberry juice is 3 cups. Scaled cranberry juice: \( 3\times4 = 12 \) cups.

Answer:

Orange juice: 16 cups, Cranberry juice: 12 cups

Part 2: Total cups of punch (from the diagram, but the question is about how many total to make? Wait, the first part is for 28 cups. Wait, maybe the diagram is for the original 7 cups (4 orange, 3 cranberry) and the question is how many total for 28? Wait, no, the first question is how many of each for 28, and the second is "How many total cups of fruit punch do you need to make?" Wait, maybe the second question is just confirming the total, which is 28. But let's check:

Wait, the problem says "How many total cups of fruit punch do you need to make?" So the answer is 28 cups.