A-C=B/2

A-B=C/6
B+C=32 find A,B,C

a - c = b/2

a -c/6 = b
-------------- subtract
-5c/6 = -b/2
b = 5 c/3

so
5 c/3 + c = 32

8 c/3 = 32

c = 12

your turn

To find the values of A, B, and C in the given equations, we can solve the system of equations using a method called substitution. Here's how to do it step by step:

1. We have three equations:
- A - C = B/2 .............(Equation 1)
- A - B = C/6 .............(Equation 2)
- B + C = 32 .............(Equation 3)

2. Let's solve Equation 3 for B:
B = 32 - C ..............(Equation 4)

3. Now, substitute Equation 4 into Equation 1:
A - C = (32 - C)/2

4. Simplify Equation 1:
2A - 2C = 32 - C

5. Rearrange the terms in Equation 1:
2A = 32 + C

6. Divide both sides of Equation 1 by 2:
A = (32 + C)/2 ...........(Equation 5)

7. Substitute Equation 4 into Equation 2:
(32 + C)/2 - (32 - C) = C/6

8. Simplify Equation 2:
(32 + C)/2 - 32 + C = C/6

9. Multiply both sides of Equation 2 by 6 to eliminate the fractions:
3(32 + C) - 192 + 6C = C

10. Expand and simplify Equation 2:
96 + 3C - 192 + 6C = C

11. Combine like terms in Equation 2:
9C - 96 = C

12. Subtract C from both sides of Equation 2:
8C - 96 = 0

13. Add 96 to both sides of Equation 2:
8C = 96

14. Divide both sides of Equation 2 by 8:
C = 96/8 ...............(Equation 6)

15. Substitute the value of C from Equation 6 into Equation 5 to find A:
A = (32 + C)/2

16. Substitute the value of C from Equation 6 into Equation 4 to find B:
B = 32 - C

17. Calculate the values of A, B, and C:
A = (32 + (96/8))/2
B = 32 - (96/8)
C = 96/8

Simplify these equations to find the final values of A, B, and C.