Question

The sum of the digits of a certain two-digit number is 7. Reversing its digits increases the number by 9. What is the number?

Answer 1

34

Luis, what are you smokin?

Answer 2

@Luis_Rivera

Answer 3

You're interpreting it wrong

Answer 4

Why would it say "increases the number by 9" rather than "7 increases by 9"?

Answer 5

It is referring to a number that we don't yet know

Answer 6

No, you're interpreting it wrong, you just don't realize it

Answer 7

I'm sorry that you don't understand that your steps are flawed.

Answer 8

only one person deserves medals

Answer 9

34
43

3 + 4 = 7

34 + 9 = 43 (reversed digits)

Answer 10

@myininaya

Answer 11

@satellite73

Answer 12

@Zarkon

Answer 13

i don't think 61 is 9 more than 16, so it is unlikely that 16 and 61 is the answer, at least not the way i read the question

Answer 14

Hey Hero... I know you mean well, but it comes off a little mean to tell someone they don't deserve medals.

Answer 15

myininaya , you always assume I'm being mean. Can I get the benefit of the doubt at least once?

Answer 16

So anyways how I interpret the problem is...
The sum of the digits of a certain two-digit number is 7. Reversing its digits increases the number by 9. What is the number?
Let d1d2 be a two-digit number (d1d2=d1*10+d2*1)
d1+d2=7
d2d1=9+d1d2 =>10*d2+d1=9+d1*10+d2
Is how I read the equation I could be wrong...
The last sentence doesn't make sense because it is talking about two different numbers.

Answer 17

The last sentence acts as if it is talking about the same numbers. Changing the order of the digits clearly gives us a difference number unless d1=d2 which it cannot since d1+d2=7
And there is no integer a such that a+a=7

Answer 18

9d2-9d1=9 => d2-d1=1
+ (d2+d1=7)
----------
2d2=8
d2=4
=> d2-d1=1=> 4-d1=1
=>d1=3
So the digit number that I come up with is d1d2=34

Answer 19

very nice

Answer 20

Thanks Hero.

Answer 21

a + b = 7
10a + b + 9 = 10b + a

9a - 9b = -9
9a = 9b - 9
a = b - 1

Plugging back into the original equation:

(b - 1) + b = 7
2b - 1 = 7
2b = 8
b = 4
a = 3

34.

Answer 22

\(34\) it is, \(3+4=7\) and \(43-34=9 \).