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? label the triple number line to show how many cups of orange juice and cranberry juice you need for more batches of fruit punch. stop when you reach 28 cups of fruit punch. orange juice (cups) 0 4 □ □ □ cranberry juice (cups) 0 3 □ □ □ fruit punch (cups) 0 7 □ □ 28

Explanation:

Step1: Find the scale factor

We know that the original total is 7 cups, and we need 28 cups. So the scale factor \( k \) is \( \frac{28}{7}=4 \).

Step2: Calculate orange juice for each batch

For orange juice, original is 4 cups per 7 - cup punch. For the next batches:

• First batch after 7 cups: \( 4\times2 = 8 \) (when total is \( 7\times2 = 14 \))
• Second batch after 14 cups: \( 4\times3 = 12 \) (when total is \( 7\times3 = 21 \))
• Third batch to reach 28: \( 4\times4 = 16 \) (when total is 28)

Step3: Calculate cranberry juice for each batch

For cranberry juice, original is 3 cups per 7 - cup punch. For the next batches:

• First batch after 7 cups: \( 3\times2 = 6 \) (when total is \( 7\times2 = 14 \))
• Second batch after 14 cups: \( 3\times3 = 9 \) (when total is \( 7\times3 = 21 \))
• Third batch to reach 28: \( 3\times4 = 12 \) (when total is 28)

Step4: Fill the number lines

• Orange Juice: After 4 (total 7), next is \( 4\times2 = 8 \) (total 14), then \( 4\times3 = 12 \) (total 21), then \( 4\times4 = 16 \) (total 28). So the boxes are 8, 12, 16.
• Cranberry Juice: After 3 (total 7), next is \( 3\times2 = 6 \) (total 14), then \( 3\times3 = 9 \) (total 21), then \( 3\times4 = 12 \) (total 28). So the boxes are 6, 9, 12.
• Fruit Punch: After 7, next is \( 7\times2 = 14 \), then \( 7\times3 = 21 \), then 28. So the boxes are 14, 21.

Answer:

• Orange Juice (cups): 8, 12, 16 (from left to right of the empty boxes)
• Cranberry Juice (cups): 6, 9, 12 (from left to right of the empty boxes)
• Fruit Punch (cups): 14, 21 (from left to right of the empty boxes)

For the amount of each juice in 28 cups: Orange juice is 16 cups, Cranberry juice is 12 cups.