Certainly! Let's understand and solve the problem step-by-step.
1. Define the Numbers:
- Let the first number be [tex]\( x \)[/tex].
2. Calculate the Second Number:
- The second number is 25% more than the first number.
- Calculating 25% of [tex]\( x \)[/tex]: [tex]\( 0.25 \times x = 0.25x \)[/tex].
- Adding this to the first number: [tex]\( x + 0.25x = 1.25x \)[/tex].
3. Calculate the Third Number:
- The third number is 50% more than the first number.
- Calculating 50% of [tex]\( x \)[/tex]: [tex]\( 0.50 \times x = 0.50x \)[/tex].
- Adding this to the first number: [tex]\( x + 0.50x = 1.50x \)[/tex].
4. Calculate What Percentage of the Second Number the Third Number Is:
- The second number is [tex]\( 1.25x \)[/tex].
- The third number is [tex]\( 1.50x \)[/tex].
- To find what percentage the third number is of the second number, use the formula:
[tex]\[
\text{Percentage} = \left( \frac{\text{Third Number}}{\text{Second Number}} \right) \times 100
\][/tex]
- Substitute the values into the formula:
[tex]\[
\text{Percentage} = \left( \frac{1.50x}{1.25x} \right) \times 100
\][/tex]
5. Simplify the Calculation:
- Simplify the fraction:
[tex]\[
\frac{1.50x}{1.25x} = \frac{1.50}{1.25} = 1.2
\][/tex]
- Therefore, the percentage is:
[tex]\[
1.2 \times 100 = 120\%
\][/tex]
So, the third number is [tex]\( 120\% \)[/tex] of the second number.
