Four different positive whole numbers sum to one hundred twenty-five. If you increase one of these numbers by four, decrease the second by four, multiply the third by four, and divide the last by four, you will produce four equivalent numbers. What is the greatest of these four numbers?

Source: mathcontest.olemiss.edu 10/14/29013

**SOLUTION**

Let represent the four whole numbers. We have the following conditions:

We use the method of substitution to solve Eq. (1) for .

Add to both sides of Eq.

Substitute the value of from Eq.

Subtract from both sides

Substitute the value of

Substitute the value of

Simplify

Calculate

Calculate

Calculate

the greatest of the four numbers.

**Answer**:

Advertisements