Math challenge problem need help please?

Question

If we start with the number 5 and put the digit 1 in front of it, we get the number 15, which is exactly threes times the original number

Can you find other numbers with the same property???

Answer 1

it is really simple.... consider x to be the number you are looking for and choose k so that:
10^k <= x < 10^(k+1)
now the solution of your problem is coming very clear: you have to find numbers that solves:
10^(k+1) + x = 3x
with simple algebra you get:
x = 5*(10^k)
for every k in N.. here u got all the solutions, and there are a infinity of them..

note: x^y means x at the power of y

Answer 2

Let your number to put a 1 in front of = X,

if X is a single digit number you get 10+X = 3X
if X is a 2 digit number you get 100 + X = 3X
if X is a 3 digit number you get 1000 + X = 3X

each of these have a seperate solution

10 = 2X
100 = 2X
1000 = 2X
and so on

in all cases X is a factor of 5 times 10 to some power, namely the number of digits X is.

5, 50, 500, etc

In general if X is a n digit number then the answer will take the form of 5*10**n

Answer 3

With one digit there is only 5
If you considerer two digits 10b+b.(putting 1 digit in front means to sum 100
you get 10a +b +100 =30a+3b and 10a+b=50 so b= 50-10a.

The only solution is a= 5 b=0 so the number would 50 and so on
500 etc

Answer 4

put 1 in front of 50 to get 150 = 3 x 50

put 1 in front of 500 to get 1500 = 3 x 500

put 1 in front of 5000 to get 15000 = 3 x 5000

etc.

There are an infinite number of solutions

Answer 5

Unclear question. What exactly is the "same property"?
Must we always start withe digit 5? Must we always prefix the starting number with 1? Must the result always be three times the start number?

Answer 6

sorry dude, we cannot have any other number like that
Prove:
Let the number we wanna find is x
the the number after we add digit 1 in front of it is 1x
But we can express 1x in the form like this...
1x = 10 + x
and as your question, 1x is 3 times of x, then:
10 + x = 3x
solve this problem we have 10 = 2x which means x = 5 the only number

Answer 7

ok shall we see... tutor that for each non-unfavorable integer n, the type 7^7^n +a million is the fabricated from a minimum of 2n+3 (no longer inevitably different) best aspects. This replaced into from the 2007 USAMO. on the competition, I merely wrote for n=0, the region is trivial. something of the data by induction is left as an workout for the grader. LOL

Answer 8

50, 500, 5000, etc...