Answer:
The numbers are 8, 1, 3
Explanation:
Let the numbers be x, y, z,
The sum of three numbers is 12
so,
x + y + z = 12
The first number is twice the sum of the second and third
x = 2(y + z)
The third number is 5 less than the first.
z = x - 5
so we get the system of equations,
x + y + z = 12 (i)
x = 2(y + z) (ii)
z = x - 5 (iii)
Solving,
putting the value of z from (iii) into (ii),
x = 2(y + z)
x = 2(y + x - 5)
x = 2y + 2x - 10
x- 2y + 10 = 2x
-2y + 10 = 2x - x
x = 10 - 2y (iv)
Putting value of x and z from (iv) and (iii) into (i),
(10 - 2y) + y + (x - 5) = 12
10 - 2y + y + (10 - 2y - 5) = 12
10 + 10 - 5 -2y -2y + y = 12
15 - 3y = 12
15 = 12 + 3y
3y = 15 - 12
3y = 3
y = 3/3
y = 1
hence the value of y is 1
Using this in (iv),
x = 10 - 2y
x = 10 - 2(1)
x = 10 - 2
x = 8
hence the value of x is 8
Using this in (iii)
z = x - 5
z = 8 - 5
z = 3
Hence the value of z is 3
The numbers are 8, 1, 3