Question

The product of a particular number and a second value, which is given by the sum of 8 and the original number, is 65. What is the number?

Answer 1

Answer:

there are infinite values of sum X + Y = (Y + 65/Y) since there are infinite values of Y.

Step-by-step explanation:

XY = 65. Given that question is asking you find X + Y, it kind of indicates that there could be very limited possible values of X and Y which you can work out. Again it is an indication of such silly questions. It need not be true that you have limited solutions.

One such solution is represented here. I have assumed X and Y are positive integers only.

Factorize 65 = 65 x 1 or 13 x 5

Therefore (X,Y) can be (65,1) or (13,5) .

So X + Y = 66 or 18.

If we include negative integers as well ,

then XY = 65 => Factors are 65 x 1, 13 x 5 or (-13) x (-5) or (-65) x (-1)

So X + Y = -66 or -18 or 18 or 66.

In general,

XY = 65 => X = 65/Y (assuming Y is not 0 else XY would have been 0 too).

Therefore X + Y = Y + 65/Y.

If X, Y belong to real or complex numbers except 0,

there are infinite values of sum X + Y = (Y + 65/Y) since there are infinite values of Y.