Certainly! Let's solve the problem step by step:
1. Understanding the Parameters:
- Genevieve has a 60-inch piece of ribbon.
- 2 inches of the ribbon are frayed, so she will start cutting from the 2-inch mark.
- She needs to divide the ribbon into a ratio of 2:3.
2. Calculate the Effective Length for Cutting:
- The total length of the ribbon is 60 inches.
- Subtract the 2 inches that are frayed, which leaves us with [tex]\( 60 - 2 = 58 \)[/tex] inches of usable ribbon.
3. Determine the Ratio Parts:
- The ratio of the sections is 2:3.
- The total number of parts in this ratio is [tex]\( 2 + 3 = 5 \)[/tex].
4. Calculate the Length of Each Part:
- The usable ribbon length is 58 inches.
- Divide this length by the number of parts to find the length of each part:
[tex]\[ \text{Length of each part} = \frac{58 \text{ inches}}{5} = 11.6 \text{ inches} \][/tex]
5. Calculate the Cut Location:
- Since Genevieve is making the cut to create the first segment which is in a ratio of 2 out of the total ratio of 5:
- The length for the first segment of the ribbon is [tex]\( 2 \)[/tex] parts long:
[tex]\[ \text{Length of the first segment} = 2 \times 11.6 \text{ inches} = 23.2 \text{ inches} \][/tex]
- Adding back the 2 inches where she started cutting guarantees:
[tex]\[ \text{Cut Location} = 23.2 \text{ inches} + 2 \text{ inches} = 25.2 \text{ inches} \][/tex]
6. Selecting the Nearest Option:
- The options provided are [tex]\( 25.2 \text{ in.}, 29.4 \text{ in.}, 35.1 \text{ in.}, 40.7 \text{ in.} \)[/tex].
- The calculated cut location, 25.2 inches, matches exactly with one of the provided choices.
Therefore, the cut will be located at 25.2 inches.
