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