To solve this problem, let's break it down into clear steps and perform each conversion and calculation.
### Step 1: Convert the initial length of ribbon from yards to inches
Anais bought [tex]\( 2 \frac{1}{2} \)[/tex] yards of ribbon.
1. Convert the mixed number [tex]\( 2 \frac{1}{2} \)[/tex] to an improper fraction:
[tex]\[
2 \frac{1}{2} = 2 + \frac{1}{2} = \frac{5}{2} \text{ yards}
\][/tex]
2. Convert yards to inches (1 yard = 36 inches):
[tex]\[
\frac{5}{2} \text{ yards} \times 36 \text{ inches per yard} = \frac{5 \times 36}{2} = \frac{180}{2} = 90 \text{ inches}
\][/tex]
So, Anais initially had 90 inches of ribbon.
### Step 2: Convert the remaining length of ribbon from feet and inches to inches
Anais had 2 feet 8 inches of ribbon left.
1. Convert the feet to inches (1 foot = 12 inches):
[tex]\[
2 \text{ feet} \times 12 \text{ inches per foot} = 24 \text{ inches}
\][/tex]
2. Add the additional 8 inches:
[tex]\[
24 \text{ inches} + 8 \text{ inches} = 32 \text{ inches}
\][/tex]
So, Anais had 32 inches of ribbon left.
### Step 3: Calculate how many inches of ribbon were used
To find out how much ribbon was used, subtract the remaining length from the initial length:
[tex]\[
90 \text{ inches (initial)} - 32 \text{ inches (remaining)} = 58 \text{ inches}
\][/tex]
Therefore, Anais used 58 inches of ribbon to trim the curtains.
Thus, the solution is:
[tex]\[ \boxed{58} \][/tex]
Anais used [tex]\(\boxed{58}\)[/tex] inches of ribbon.
