Question

If the mean of A and B is 20, the mean of B and C is 24 and the mean of A,B and C is 18.What is the mean of A and C?

Answer 1

the mean of A and C is 10

Explanation:

Given;

mean of A and B = 20

mean of B and C = 24

mean of A, B and C = 18

`(A + B)/(2) = 20\\\\A+ B = 40 ---- (1)\\\\(B + C)/(2) = 24\\\\B+ C = 48----(2)\\\\(A+ B+ C)/(3) = 18\\\\A+ B+ C= 54---(3)\\\\From (1); \ A = 40 - B\\\\From(2); \ C = 48 - B\\\\\Substitute \ the \ values \ of \ A \ and \ C \ into \ (3)\\\\(40-B) + B + (48-B) = 54\\\\simplify;\\\\(40 + 48) + (B-B-B)= 54\\\\88 -B = 54\\\\-B = 54-88\\\\-B = -34\\\\B = 34`

Recall; A = 40 - B

A = 40 - 34

A = 6

Also, C = 48 - B

C = 48 - 34

C = 14

Therefore, the mean of A and C is calculated as;

`= (A + C)/(2) \\\\= (6 + 14)/(2) \\\\= 10`