Question

The sum of three numbers is 12. The second number is equal to the sum of the first and third numbers. Twice the first number exceeds the second number by 4. Find the numbers.

Answer 1

the first number is 5

the first second is 6

the first number is 1

Explanation:

x - first number

2x - twice the first number

twice the first number exceeds the second number by 4 so:

2x-4 -the second number

y - the third number

the second number is equal to the sum of the first and third numbers:

2x-4 = x + y

x + y = 2x - 4

-x -x

y = x - 4 - the third number

the sum of three numbers:

x + 2x-4 + x-4 = 4x - 8

The sum of three numbers is 12 so:

4x - 8 = 12

+8 +8

4x = 20

÷4 ÷4

x = 5

2x-4 = 2•5 - 4 = 6

x-4 = 5 - 4 = 1

Check:

5+1 = 6

2•5 = 10, 10-4 = 6