College

Emily is making bows using ribbon. She has two pieces of ribbon to use. One piece is 23 yards long, and the length of the other piece is unknown. She needs [tex]$1 \frac{5}{6}$[/tex] yards of ribbon to make each bow. What is the greatest number of bows Emily can make?

A. 12
B. 14
C. 15
D. 19

Answer :

To solve the problem of determining the greatest number of bows Emily can make, let's go through the process step-by-step.

1. Understand the Problem:
- Emily has a ribbon that is 23 yards long.
- She needs [tex]\(1 \frac{5}{6}\)[/tex] yards of ribbon to make each bow.

2. Convert the Mixed Number to an Improper Fraction:
- [tex]\(1 \frac{5}{6}\)[/tex] can be expressed as an improper fraction. [tex]\(1 \frac{5}{6} = \frac{11}{6}\)[/tex].

3. Calculate the Total Length of Ribbon Required for One Bow:
- Each bow requires [tex]\(\frac{11}{6}\)[/tex] yards of ribbon.

4. Determine How Many Full Bows Can Be Made:
- We need to determine how many times the length of ribbon needed for one bow ([tex]\(\frac{11}{6}\)[/tex] yards) can fit into the total length of the ribbon (23 yards).
- To find this, divide the total ribbon (23 yards) by the ribbon needed per bow ([tex]\(\frac{11}{6}\)[/tex] yards).
- In fractional form, this division is:
[tex]\[
23 \div \frac{11}{6} = 23 \times \frac{6}{11} = \frac{138}{11} \approx 12.545
\][/tex]
- Since Emily cannot make a fraction of a bow, she can only make a whole number of bows. Thus, she can make 12 full bows.

Therefore, the greatest number of bows Emily can make is 12.