Sure, let's work through the problem step-by-step.
We need to rewrite the ratio [tex]\(15:54\)[/tex] in the form [tex]\(1:n\)[/tex]. Here's how we can do that:
1. Understand the Given Ratio:
The given ratio is [tex]\(15:54\)[/tex]. This means for every 15 parts of the first quantity, there are 54 parts of the second quantity.
2. Convert the Ratio to the Form [tex]\(1:n\)[/tex]:
To convert the given ratio into the form [tex]\(1:n\)[/tex], we need to determine what [tex]\(n\)[/tex] would be if the first part of the ratio were 1.
For this, we divide both terms of the ratio by 15 (the first part of the given ratio).
[tex]\[
\frac{54}{15}
\][/tex]
3. Calculate the Value of [tex]\(n\)[/tex]:
Perform the division to find the value of [tex]\(n\)[/tex]:
[tex]\[
n = \frac{54}{15} = 3.6
\][/tex]
4. Express the Ratio:
Now that we have [tex]\(n\)[/tex], we can express the ratio [tex]\(15:54\)[/tex] in the desired form [tex]\(1:n\)[/tex]:
[tex]\[
15:54 = 1:3.6
\][/tex]
So the equivalent ratio of [tex]\(15:54\)[/tex] in the form [tex]\(1:n\)[/tex] is [tex]\(1:3.6\)[/tex], with [tex]\(n = 3.6\)[/tex].
