Question

Three whole numbers are chosen with a mean of 10 and a range of 4. Can you determine the numbers?

Answer 1

Numbers are:

x1 , x2 , x3

The mean is the average of the numbers.

In this case:

mean = ( x1 + x2 + x3 ) / 3

( x1 + x2 + x3 ) / 3 = 10

Multiply both sides by 3.

x1 + x2 + x3 = 30

The range is the difference between the highest and lowest values in a set of numbers.

Suppose the numbers are written so that x1 is the lowest number and x3 is the highest number.

range = x3 - x1

In thus case:

x3 - x1 = 4

Add x1 to both sides

x3 = x1 + 4

Put this value in equation:

x1 + x2 + x3 = 30

x1 + x2 + x1 + 4 = 30

2 x1 + x2 + 4 = 30

Subtract 4 to both sides

2 x1 + x2 = 26

Now you have a system of TWO equations:

x1 + x2 + x3 = 30

2 x1 + x2 = 26

This system have THREE unknowns:

x1 , x2 , x3

This means that you need one more condition to solve the system.

Check did you wrote the question correctly.