# Answer on Combinatorics | Number Theory Question for gajendra

Question #28608

Identify the number that is equal to five times the sum of the digits.

Expert's answer

1) Assuming that our two-digit number is ( x + y*10) , where y -the first digit , x - the second digit. And we know that (x+y)*5 must be equal to x + y*10.

2)So we have equation:

(x+y)*5 = x + 10y

5x + 5y = x + 10y

5x = x +10y - 5y

5x = x + 5y

5x - x = 5y

4x = 5y

0.8x = y

3) All digits must be integer , that's why x=5 , because it is the only digit that can make y integer. And we have y= 0.8*5 = 4.

Let's check the answer (4+5)*5 = 45 ALL RIGHT.

ANSWER IS 45

2)So we have equation:

(x+y)*5 = x + 10y

5x + 5y = x + 10y

5x = x +10y - 5y

5x = x + 5y

5x - x = 5y

4x = 5y

0.8x = y

3) All digits must be integer , that's why x=5 , because it is the only digit that can make y integer. And we have y= 0.8*5 = 4.

Let's check the answer (4+5)*5 = 45 ALL RIGHT.

ANSWER IS 45

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