Question

The sum of three numbers is 70 . The third number is 2 times the first. The first number is 6 less than the second. What are the numbers?

Answer 1

16, 22, and 32.

Explanation:

Set up a system of equations to represent the situation with 3 unknown.

x + y + z = 70

z = 2x

x = y - 6 → y = x + 6

The second two equations are the y and z in terms of x, so substitute both into the first equation.

x + (x + 6) + 2x = 70

4x + 6 = 70

4x = 64

x = 16

Use this number to calculate the value of the other unknowns.

y = x + 6

y = 16 + 6

y = 22

Calculate z.

z = 2x

z = 2(16)

z = 32

So, the three numbers are 16, 22, and 32.