Question

Write down three integers,all less than 25,whose range is 10 and mean is 13.

Answer 1

Let a,b ,c be an integer numbers such that each is less than 25, their mean is 13 and range - 10.

1. Let a<b<c<25;

2. $\dfrac{a+b+c}{3} =13 \\ a+b+c=39$

3. c-b=b-a=10.
Then
 $c=10+b \\ a=b-10 \\ b-10+b+10+b=39 \\ b=13, c=23, a=3$.
Answer: a=3, b=13, c=23.

Answer 2

Let
x------> the first integer
y------> the second integer
z-----> the third integer

x < y < z < 25

we know that
Median=13
Median=(x+y+z)/3
13=(x+y+z)/3
x+y+z=39------> equation 1

range=10
The range is the difference between the largest number within the set and the smallest number in the set
so
range=z-x
z-x=10------> z=x+10-----> equation 2


to find the solution we will assume different values ​​of x (See the attached table)   
terms
x < y < z < 25
z=x+10
y=39-z-x

The solution can be
7,15,17
8,13,18
9,11,19