Help me please.

[Jheisra]

Please answer this.
One number is three times another and their product is equal to their sum increases by fifty five find the number

[[email protected]]

Hi Jheisra,

What is the source of this question? Is it from a GMAT source or a 'math book?' I ask because the wording is clunky and you have not included the 5 answer choices. The math is based on Quadratic Algebra, so there are actually 2 solutions. As it stands, having those 5 answers would make solving this question REALLY easy. Without them though, we're almost forced to take a 'math heavy' approach.

With the information that we've been given, we can form the following equation (we can refer to the numbers as X and 3X):

(X)(3X) = (X+3X) + 55

3X^2 = 4X + 55

From here, we can solve Algebraically or use 'brute force' (and if we had 5 answer choices, then we could TEST THE ANSWERS).

Algebraically:
3X^2 - 4X - 55 = 0
(X - 5)(3X + 11) = 0
X = 5 or - 11/3

GMAT assassins aren't born, they're made,
Rich

[regor60]

And it seems likely by the wording that the "number" requested is then 15 or -11

[Matt@VeritasPrep]

a 'math book?'

Do we mean an actual math book, or a phony math book? Seems like real math to me, no quotations required.

[Matt@VeritasPrep]

We've got

a = 3b

and

a*b = a + b + 55

so

3b² = 4b + 55

3b² - 4b - 55 = 0

(3b + 11)(b - 5) = 0

b = 5 or b = -11/3

from which

a = 15 or a = -11