Answer :
Sure! Let's solve this step-by-step.
We are given that [tex]\(\frac{1}{4}\)[/tex] of Zara's ribbon is the same length as [tex]\(\frac{1}{3}\)[/tex] of Sofia's ribbon. We need to determine whose ribbon is shorter.
1. Set up the relationship:
Since [tex]\(\frac{1}{4}\)[/tex] of Zara's ribbon is equal to [tex]\(\frac{1}{3}\)[/tex] of Sofia's ribbon, we can write this as an equation:
[tex]\[
\frac{1}{4} \times \text{(length of Zara's ribbon)} = \frac{1}{3} \times \text{(length of Sofia's ribbon)}
\][/tex]
Let's denote the length of Zara's ribbon as [tex]\(z\)[/tex] and the length of Sofia's ribbon as [tex]\(s\)[/tex].
So, we have:
[tex]\[
\frac{1}{4}z = \frac{1}{3}s
\][/tex]
2. Solve for the relationship between [tex]\(z\)[/tex] and [tex]\(s\)[/tex]:
To find out the relationship between [tex]\(z\)[/tex] and [tex]\(s\)[/tex], solve the equation:
[tex]\[
\frac{1}{4}z = \frac{1}{3}s
\][/tex]
Multiply both sides of the equation by 12 to eliminate the fractions:
[tex]\[
12 \times \frac{1}{4}z = 12 \times \frac{1}{3}s
\][/tex]
Simplifying both sides gives:
[tex]\[
3z = 4s
\][/tex]
3. Determine which ribbon is longer:
Now, solve for [tex]\(z\)[/tex] in terms of [tex]\(s\)[/tex]:
[tex]\[
z = \frac{4}{3}s
\][/tex]
This means that Zara's ribbon is [tex]\(\frac{4}{3}\)[/tex] times the length of Sofia's ribbon. Since [tex]\(\frac{4}{3}\)[/tex] is greater than 1, Zara's ribbon is longer than Sofia's ribbon.
Conclusion: Sofia's ribbon is shorter.
We are given that [tex]\(\frac{1}{4}\)[/tex] of Zara's ribbon is the same length as [tex]\(\frac{1}{3}\)[/tex] of Sofia's ribbon. We need to determine whose ribbon is shorter.
1. Set up the relationship:
Since [tex]\(\frac{1}{4}\)[/tex] of Zara's ribbon is equal to [tex]\(\frac{1}{3}\)[/tex] of Sofia's ribbon, we can write this as an equation:
[tex]\[
\frac{1}{4} \times \text{(length of Zara's ribbon)} = \frac{1}{3} \times \text{(length of Sofia's ribbon)}
\][/tex]
Let's denote the length of Zara's ribbon as [tex]\(z\)[/tex] and the length of Sofia's ribbon as [tex]\(s\)[/tex].
So, we have:
[tex]\[
\frac{1}{4}z = \frac{1}{3}s
\][/tex]
2. Solve for the relationship between [tex]\(z\)[/tex] and [tex]\(s\)[/tex]:
To find out the relationship between [tex]\(z\)[/tex] and [tex]\(s\)[/tex], solve the equation:
[tex]\[
\frac{1}{4}z = \frac{1}{3}s
\][/tex]
Multiply both sides of the equation by 12 to eliminate the fractions:
[tex]\[
12 \times \frac{1}{4}z = 12 \times \frac{1}{3}s
\][/tex]
Simplifying both sides gives:
[tex]\[
3z = 4s
\][/tex]
3. Determine which ribbon is longer:
Now, solve for [tex]\(z\)[/tex] in terms of [tex]\(s\)[/tex]:
[tex]\[
z = \frac{4}{3}s
\][/tex]
This means that Zara's ribbon is [tex]\(\frac{4}{3}\)[/tex] times the length of Sofia's ribbon. Since [tex]\(\frac{4}{3}\)[/tex] is greater than 1, Zara's ribbon is longer than Sofia's ribbon.
Conclusion: Sofia's ribbon is shorter.