vaibhav101 wrote:a trussian's weight , in Keils , can be calculated by taking the square root of his age in years. A Trussian's teenager now weighs 3 Keils less than he will 17 years after he is twice as old as he is now. How old is he now?
A 14
B 15
C 16
D 17
E 18
We can let his current age = x and create the following equation:
√x = √(2x + 17) - 3
√x + 3 = √(2x + 17)
Squaring both sides, we have:
x + 6√x + 9 = 2x + 17
6√x = x + 8
Squaring both sides again, we have:
36x = x^2 + 16x + 64
x^2 - 20x + 64 = 0
(x - 4)(x - 16) = 0
x = 4 or x = 16
Since only 16 is given in the answer choices, then C is the correct choice.
Alternate solution:
Since the problem involves taking the square root of a number, and 16 is the only number in the answer choices that is a perfect square, we can guess that 16 is the correct answer. We only need to verify that it is the correct answer.
If the Trussian's current age is 16, then his weight would be √16 = 4 Keils.
17 years after he is twice as old, his age will be 17 + 2(16) = 49 and his weight will be √49 = 7 Keils.
Since 4 is 3 less than 7, we see that we have guessed correctly.
Answer: C
