The average (arithmetic mean) of A and B is 10, whereas the average of B and 10 is C/2. What is the average of A and C?

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- Jan 25th 2007, 12:05 PMceasar_19134The average of A and B is 10...
The average (arithmetic mean) of A and B is 10, whereas the average of B and 10 is C/2. What is the average of A and C?

- Jan 25th 2007, 12:08 PMThePerfectHacker
This looks like a SAT question.

$\displaystyle \frac{A+B}{2}=10$

$\displaystyle \frac{B+10}{2}=\frac{C}{2}$

Thus,

$\displaystyle A+B=20$ (1)

$\displaystyle B+10=C$ (2)

From (1) subtract (2),

$\displaystyle A-10=20-C$

$\displaystyle A+C=30$

$\displaystyle \frac{A+C}{2}=15$