AM between two numbers whose sum is 100 is ti the GM as ``5:4`, find the numbers.

Explanation

To solve the problem step by step, we need to find two numbers \( a \) and \( b \) such that their sum is 100, and the ratio of their Arithmetic Mean (AM) to their Geometric Mean (GM) is \( \frac{5}{4} \).

### Step 1: Set up the equations
Given:
- \( a + b = 100 \)
- The ratio of AM to GM is \( \frac{5}{4} \)

The Arithmetic Mean (AM) of \( a \) and \( b \) is given by:
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