The sum of three numbers is 26 .twice the first minus the second is 2 less than third. the third is the second minus three times the first find the numbers.

Question

How do I figure out the equations?

Answer 1

A = first number

B = second number

C = third number

 

1) A + B + C = 26

 

2) 2A - B = C-2

 

3) C = B - 3A  

 

There are several approaches. Here is one of them:       

 

Express equation 2) as C

4) C = 2A - B + 2

 

Now equation 3 equals equation 4

5) B - 3A = 2A - B + 2

 

Solve equation 5) for B

6) 2B = 2A + 3A + 2

    B = 2A/2 + 3A/2 +2/2

    B = A + 1.5A + 1

    B = 2.5A + 1

 

Substitute this definition of B into equation 3)

3) C = B - 3A

7) C = (2.5A + 1) - 3A

 

Now we have B and C expressed in terms of A and we go back to equation 1).

 

A + B + C = 26

A + (2.5A + 1) + (2.5A + 1 - 3A) = 26

A + 5A - 3A + 2 = 26

3A = 26 - 2

A = 24/3

A = 8

 

Now work you way through the other equations to find that B = 21 and C = -3