There are three numbers: x, y, and z. the sum of these three numbers is 24. the second number is five times the first number. the third number is twice as much as the second number. find each variable's value.

The three numbers are x, y, z
The sum of the three numbers = x + y + z = 24

Let the first number = x
The second number is five times the first number = y = (x + 5)
The third number is twice as much as the second number = z = 2y = 2(x + 5)

The sum of these numbers = 24
x + y + z = 24

Substituting the values of y and z in terms of x

x + (x + 5) + 2(x + 5) = 24
x + x + 5 + 2x + 10 = 24
4x + 15 = 24
4x = 24 - 15
4x = 9
x = 9 ÷ 4
x = 2.25

Therefore,
x = 2.25
y = (x + 5) = 2.25 + 5 = 7.25
z = 2(x + 5) = 2(2.25 + 5) = 2 x 7.25 = 14.5

Sum of the three numbers = x + y + z = 2.25 + 7.25 + 14.5 = 24