To solve the problem where 20% of a number is 27 and we need to find [tex]\(\frac{1}{3}\)[/tex] of that number, we can follow these steps:
1. Understand the Problem: We are given that 20% of a certain number equals 27. We need to find the total number and then determine one-third of that number.
2. Convert the Percentage to a Decimal:
[tex]\[
20\% = \frac{20}{100} = 0.20
\][/tex]
3. Set Up the Equation:
Let's denote the unknown number by [tex]\( x \)[/tex]. According to the problem:
[tex]\[
0.20 \times x = 27
\][/tex]
4. Solve for [tex]\( x \)[/tex]:
To find [tex]\( x \)[/tex], we divide 27 by 0.20:
[tex]\[
x = \frac{27}{0.20}
\][/tex]
5. Calculate the Value of [tex]\( x \)[/tex]:
[tex]\[
x = 135
\][/tex]
6. Find One-Third of the Number:
Now that we know the number is 135, we need to find [tex]\(\frac{1}{3}\)[/tex] of 135:
[tex]\[
\frac{1}{3} \times 135 = 45
\][/tex]
So, [tex]\(\frac{1}{3}\)[/tex] of the number is 45.
