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

`\frac{a_1+a_2+a_3+a_4}4=40`

`a_1+a_2+a_3+a_4=160`

`\frac{a_1+a_2+a_3}3+\frac{a_4}3=\frac{160}3`

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

`\frac{a_4}3=\frac{160}3-42`

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