The Michigan papyrus 620 is a Greek papyrus written in the second century. It contains three arithmetic problems. One of these problems follows:

Four numbers: their sum is 9900; let the second exceed the first by one-seventh of the first; let the third exceed the sum of the first two by 300; and let the fourth exceed the sum of the first three by 300. Find the four numbers.

Source: mathcontest.olemiss.edu 4/30/2007

**SOLUTION
**Let be the four numbers. Let’s represent the first number as an apple pie divided into 7 equal pieces as follows:

We don’t know the numerical value of each piece. If we do, we will know the value of . All we know is that

Because the second number exceeds the first number by one-seventh of the first,

The third number exceeds the sum of the first two by 300,

The fourth number exceeds the sum of the first three by 300,

The sum of the four numbers is 9900,

Subtracting 900 from both sides,

Now we can compute the value of the numbers:

**Check
**

**Answer**: 1050, 1200, 2550, 5100.