1977 AHSME Problems/Problem 12
Al's age is more than the sum of Bob's age and Carl's age, and the square of Al's age is more than the square of the sum of Bob's age and Carl's age. What is the sum of the ages of Al, Bob, and Carl?
Solution by e_power_pi_times_i
Denote Al's age, Bob's age, and Carl's age by , , and , respectively. Then, and . Substituting the first equation into the second, . Thus, , and . Since , or . Then .