Question

90n+23p=4523
If n and p are positive integers in the equation above, what is one possible value of n+p?

Answer 1

In this problem you would just plug in some of the possible answers.

Answer 2

I would start with the answers that have small factors

Answer 3

it's not multiple choice though, so is there any time efficient ways?

Answer 4

*are there

Answer 5

90n = 4523 -23p
90n = 4500 +23 -23p
90n = 4500 +23 (1-p)
Now in this equation we can plug p = 1 and get n = 50
so one solution of n+p = 51

Answer 6

We could work it further for more solutions
90n = 4500 +23(1-p)
90n-4500 = 23 (1-p)
90(n-50) = 23 (1-p)
\[n-50 = \frac{23 (1-p)}{90}\]
Since n and p are both integers n-50 should also be an integer
Thus we may say that 23(1-p) should be a multiple of 90
this condition is met only when (1-p) = 0 or 90 or 180 or 270 and so on.
so you may get as many values from this condition as you want.

Answer 7

hmm ok cool thanks!