Let's solve this problem step by step.
1. Convert the total amount of ribbon from yards to inches:
Anais bought [tex]\(4 \frac{1}{2}\)[/tex] yards of ribbon. To work with this more easily, let's convert it to a decimal:
[tex]\[
4 \frac{1}{2} = 4.5 \text{ yards}
\][/tex]
Since 1 yard equals 36 inches, we convert 4.5 yards to inches:
[tex]\[
4.5 \text{ yards} \times 36 \text{ inches/yard} = 162 \text{ inches}
\][/tex]
2. Convert the remaining ribbon from feet and inches to inches:
Anais had 3 feet 8 inches of ribbon left. We first convert the feet to inches:
[tex]\[
3 \text{ feet} \times 12 \text{ inches/foot} = 36 \text{ inches}
\][/tex]
Then we add the additional 8 inches:
[tex]\[
36 \text{ inches} + 8 \text{ inches} = 44 \text{ inches}
\][/tex]
3. Determine how many inches of ribbon were used by subtracting the remaining ribbon from the total ribbon:
We know the total amount of ribbon was 162 inches and there are 44 inches left:
[tex]\[
162 \text{ inches} - 44 \text{ inches} = 118 \text{ inches}
\][/tex]
Anais used [tex]\( 118 \)[/tex] inches of ribbon to trim the curtains.
The solution is [tex]\( \boxed{118} \)[/tex].
