Given : ( A and B ) = 20 , ( B and C ) = 24 , ( A, B and C ) = 18
Ask : ( A and C ) = ?
Solution :
mean of :
A + B is 40 since ( A + B ) / 2 = 20 ( 1st Equation )
B + C is 48 since ( B + C ) / 2 = 24 ( 2nd Equation )
A + B + C is 54 since ( A + B + C ) / 3 = 18 ( 3rd Equation )
Find B:
A + B = 40
B = 40 - A
Find C:
B + C = 48
C = 48 - B
Substitute the value of B and C to the 3rd Equation to find B:
A + B + C = 54
A + ( 40 - A ) + ( 48 - B ) = 54
A + 40 - A + 48 - B = 54
88 - B = 54
- B = 54 - 88 ( Addition Property of Equality )
- B = - 34
B = 34 (dividing both sides by - 1 )
Substitute the value of B to get A:
A + B = 40
A + 34 = 40
A = 6
Substitute the vlue of B to the 2nd Equation to get C:
B + C = 48
34 + C = 48
.
Then, the mean of A + C is 10.