Brain Jobling Math Problem?

Question

hello, need help with problem.
The product of the ages of three children is 1872. The childrens ages are equally spaced. What are the three ages.

Thanks

Answer 1

Let the ages = x, x+n, x+2n (since they are evenly spaced; notice that there is a difference of "n" in each age based on the way we just wrote them)

So we know that x*(x+n)*(x+2n) = 1872. Let's multiply and solve:

x(x+n)(x+2n) = 1872

x³ + 3nx² + 2n²x = 1872

x³ + 3nx² + 2n²x - 1872 = 0

This is looking icky. At this point, I'd switch gears and look at the factors of 1872:

1872 = 2 * 2 * 2 * 2 * 3 * 3 * 13

Now I'd try to see if I can get three numbers from these factors such that the three numbers are evenly spaced. Clearly 13 needs to be one of these numbers. From the remaining factors, I get 8 and 18.

ANSWER: 8 * 13 * 18 = 1872

{{ I'm leaving all this in, including my initial false start, so that you can see the "thought process" in action for solving HW problems. Sometimes you go down one road, and you will either succeed or you will see that it gets icky (like it did here for me), at which point you need to switch gears in your brain and attack the problem in another manner, like I did with the factoring, which luckily worked out for us. }}

Answer 2

The ages are 8, 13, and 18.
Each are 5 years apart.
8 * 13 * 18 = 1872

Answer 3

I love August, I just have to say that is an awesome solution. I never would have thought of that technique.