Question

The average age three people running for election is 42. A fourth person joins the race and the average drops to 40. What is the fourth person's age?

Answer 1

Let $a_1,\ldots,a_4$ denote the ages of the 4 candidates. Then

$\dfrac{a_1+a_2+a_3+a_4}4=40$

$a_1+a_2+a_3+a_4=160$

$\dfrac{a_1+a_2+a_3}3+\dfrac{a_4}3=\dfrac{160}3$

The average age of the first 3 candidates is 42, so

$\dfrac{a_4}3=\dfrac{160}3-42$

$\implies\boxed{a_4=160-3\cdot42=34}$