To solve this problem, let us first assign some variables.
Let us say that the numbers are:
x = the variable representing the first number
y = the variable representing the second number
z = the variable representing the third number
From the given problem, we know that:
x + y + z = 102 --->
1
z = 4 x --->
2
x = y + 6 --->
3
Rewriting equation 3 in terms of y:
y = x – 6 ---> 4
Combining equations 1, 2 and 4 to express solely on x:
x + (x – 6) + (4 x) = 102
6 x – 6 = 102
6 x = 108
x = 18
From equation 2:
z = 4 (18)
z = 72
From equation 4:
y = 18 – 6
y = 12
Hence, the numbers are:
x = 18
y = 12
z = 72
