Let R be the length of the red ribon and let I be the length of the indigo ribbon. We have that the red ribbon is 6 1/4 inches long, then:
![R=6(1)/(4)=(25)/(4)](https://img.qammunity.org/2023/formulas/mathematics/college/zh9pyohyh6lpqk61mmvmcv4tvqgp4mgyui.png)
Then, the indigo ribbon is 6 1/4 inches longer than the red ribbon. Then we have:
![I=R+6(1)/(4)](https://img.qammunity.org/2023/formulas/mathematics/college/sryzbempxogn7ej05b24n8y209t1ixri1q.png)
therefore:
![I=(25)/(4)+(25)/(4)=(50)/(4)=(25)/(2)=12(1)/(2)](https://img.qammunity.org/2023/formulas/mathematics/college/7ryhrdpijzdkthb4f27ouryior4akyeqf7.png)
finally, we have that the indigo ribbon is 12 1/2 inches long