Question

Two positive integers are in ratio 1:3. If their sum is added to their product, the result is 224. Find the integers.
On my own, I came up with the formula 224 = x + 3 x + 3x^2 but it's not really working out. Could someone please help me?

Answer 1

Your formula is correct.
Assuming you add up the 3x and x to form 4x, you have to use the general solution of a quadratic equation. Do you know how to use it? =)
By the way, x should be 8 if you use it right.

Answer 2

no, I don't think I do. I tried completing the square and I'm just getting really weird numbers. :(

Answer 3

Okay, we'll do it by completing the square. :)
From 3x^2 + 4x = 224,
x^2 + 4/3 x = 224/3
x^2 + 4/3x + 4/9 = 224/3 + 4/9
(x+2/3)^2 = 75/1/9
x + 2/3 = square root of 75/1/9
x + 2/3 = 8/2/3 or -8/2/3
x = 8 or -9/1/3( Not applicable as positive integer cannot be a negative fraction)
Hence, x = 8.
There you go! :)

Answer 4

thanks! :D

Answer 5

You're welcome ^^ :)