Question

a two-digit number is three times the sum of its digits. when the number is subtracted from the number obtained by reversing the digits, the result is 45. find the original number.

Answer 1

A=(3(B+C))
A-Reverse of same no.?45?=45
We know A is double digit and <100, therefore
A+45 = 99
99 = 3(33)
Therefore A = 99?

Answer 2

If you reverse 99 you get 99 and so 99-99=0, not 45

Answer 3

I think perhaps this formulation will help:
\[(B+C)-(10C+\frac{ B }{ 10 }) = 45\]

Using with the formulation given by Sgreborn of A=(3B+C))

Try that?

Answer 4

Sorry dont quite understand the number part "when the number is subtracted from the number obtained by reversing the digits"

Answer 5

i.e. 80-08=45 => 80-8=45 false

Answer 6

I got 27

3(2+7)=27
27-72=-45

But its negative is this right?

Answer 7

a = the tens digit
b = the ones digit

10a + b (the two digit number
a + b (the sum of its digits

10a + b = 3(a + b)
10a + b = 3a + 3b
10a - 3a = 3b - b
7a = 2b

we know that b must be 0,1,2,3,4,5,6,7,8,9 because b is a single digit
we know that a must be 1,2,3,4,5,6,7,8,9 , it can't be 0 because it is the first digit of a two digit number.

The only thing that satisfies 7a = 2b are a = 2 and b = 7
7(2) = 2(7) : 14 = 14

the number is 27.

check...
3 times the sum of its digits = 3 (7 + 2) = 3(9) = 27
when the number is subtracted from the number obtained from reversing the digits, the result is 45....27 reversed is 72 - 27 = 45

your number is 27 :)

Answer 8

@texaschic101 thanks! We got the same answer :D

Answer 9

yes we did....nice job :)