A number exceeds its three-eighths (3/8) part by 25. What is the number?

When a problem states that a number exceeds a given fractional part of itself by a fixed amount, translate it directly into a linear equation: if the number is x and the fraction is k, the condition becomes x minus k times x equals the stated excess, which can then be simplified and solved for x.

1. Let the required number be x. Its three-eighths part is (3/8)x, and the number exceeds this part by 25, giving the equation x - (3/8)x = 25.

2. Rewrite x with a denominator of 8 so both terms combine: 8x/8 - 3x/8 = 25.

3. Combine the like terms on the left-hand side: 5x/8 = 25.

4. Multiply both sides by 8 to clear the denominator: 5x = 200.

5. Divide both sides by 5 to isolate x: x = 40.

Cross-check: three-eighths of 40 is 15, and 40 minus 15 equals 25, exactly the excess stated in the question, confirming x = 40.