Final answer:
To find the longer piece of the ribbon, add the ratio parts, divide the total length by the total parts to find one part, then multiply by 7 (since the longer piece corresponds to 7 parts of the ratio), resulting in (7v + 28) / 10 feet.
Step-by-step explanation:
The student is asking about dividing a ribbon of length (v + 4) feet into two pieces in a ratio of 3:7. To find the length of the longer piece, we will first add the parts of the ratio together (3 + 7 = 10 parts in total). Then, we divide the total length of the ribbon by 10 to find the length of one part. One part would therefore be (v + 4) feet / 10. Since the longer piece is 7 parts of the ratio, the length of the longer piece would be 7 times the length of one part, which is 7 × ((v + 4) feet / 10) or simplifying, (7v + 28) / 10 feet.