Question

The first number plus the third number is equal to the second number. The sum of the first number and the second number is six more than the third number. Three times the first number minus two times the second number is equal to the third number. What is the sum of the three numbers?

Answer 1

I'll use x, y, and z for the numbers
x + z = y
x + y = 6 + z
3x - 2y = z

Substitute (x + z) for y in the second equation.
x + (x + z) = 6 + z and solve
2x = 6
x = 3

Rearrange another equation and substitute (3) for x.
(3) + y = 6 + z solve for y
y = 3 + z
substitute y in another equation
3(3) - 2(3+z) = z solve
9 - 6 - 2z = z
3 = -z
z = 3

going back to the first equation:
x+z=y
3 + 3 = 6
Answers:
x=3
y=6
z=3
check all equations to make sure it works for all equations

Answer 2

8

Explanation:

Let the first number be x

Let the second number be y

Let the third number be z

According to question

First number + third number= second Number

x + z = y equation (1)

first number + second number = 6 more than third number

x + y = 6 + z equation(2)

Put y = x + z in equation (2)

x + x + z = 6 + z

2 x = 6

x = 3

now , y = 3+z

3 times first number - 2 times second number= third number

3 x - 2 y = z equation (3)

put y = 3 +z in equation (3)

3× 3 - 2(3+z) = z

9 - 6 -2 z = z

z+2 z= 3

3 z= 3

z= 1

Now, y = 3+1= 4

Sum of x ,y and z

x+y+z= 3+4+1= 8

Hence, the correct answer is 8