Question

Which number is greater and by how much?
a positive number a, or the same number a decreased by 50% and then increased by
50% of the result

Answer 1

Let's denote the positive number as \( a \).

1. **Step 1: Decrease \( a \) by 50%:**
\[
a - 0.5a = 0.5a
\]

2. **Step 2: Increase the result by 50%:**
To find 50% of \( 0.5a \):
\[
0.5 \times 0.5a = 0.25a
\]
Now, add this to \( 0.5a \):
\[
0.5a + 0.25a = 0.75a
\]

Now we have two values to compare:
- The original number: \( a \)
- The modified number: \( 0.75a \)

**Comparison:**
- Since \( a \) is a positive number, it is clear that \( a > 0.75a \).

**Difference:**
To find out by how much \( a \) is greater than \( 0.75a \):
\[
a - 0.75a = 0.25a
\]

**Conclusion:**
The original number \( a \) is greater than \( 0.75a \) by \( 0.25a \).