The sum of the digits of a two-digit number is 9 less than the number. Which of the following digits is at?

Question

than the number. Which of the following digits is at unit’s place of the number

choice
a) 1
b) 2
c) 4
d) 8
e) None

Answer 1

The digit at units place can be anything from 1 to 9.

Let the digits be x and y
so the number is 10x+y
x+y = 10x+y -9
9x =9
so x=1

These equations are true for all values of y.
1, 2,4 , 8 all can be answers.

the digit at units place can be anything from 1 to 9.

Answer 2

Let the number be 10x + y.
The digits are x and y.

x + y = 10x + y - 9

Cancel out y from both sides.

x = 10x - 9
-9x = -9
x = 9

The tens digit is 9.
But this is not what we want.

Now in the equation, we can see that y cancels, so y can be any one - digit. a, b, c and d are all right.

You can see that any number from 10 - 19 will satisfy the condition. Only these numbers will satisfy the condition as we get x = 1

10
1 + 0 = 10 - 9 = 1

11
1 + 1 = 11 - 9 = 2

12
1 + 2 = 12 - 9 = 3

13
1 + 3 = 13 - 9 = 4

14
1 + 4 = 14 - 9 = 5

15
1 + 5 = 15 - 9 = 6

16
1 + 6 = 16 - 9 = 7

17
1 + 7 = 17 - 9 = 8

18
1 + 8 = 18 - 9 = 9

19
1 + 9 = 19 - 9 = 10

Answer 3

If you want your son to actually understand how to do these types of problems: Step 1: Set up equations Let "x" stand for the ten's place, and "y" stand for the one's place; We know that; x = y Now let "n" stand for the ten-thousands place; 3(x + y) - 1 = n Step 2: System of equations x = y 3(x + y) - 1 = n Step 3: Logic We know that "n" has to be a number less than or equal to 9, because "n" is a single digit. We also have placed restrictions on "n" that say "n" is either 4 or 5. ('Number greater than 40,000 less than 60,000') Using this logic we can deduce that x and y have to be equal to one. This is because of our second equation in the system; 3(x + y) - 1 = n If we put 2 in for x and y we get "n" = 11 This is not possible; Our only option is x and y = 1; 3(1 + 1) - 1 = n 3(2) - 1 = n 6 - 1 = n 5 = n Now we have three of our five digits; x , y = 1 n = 5 'My thousands digit is half my hundreds digit and the sum of those two digits is 9.' Let "u" stand for the thousands digit, and "v" stand for the hundreds digit; u + v = 9 u = (1/2)v If we put (1/2)"v" in for "u" in our first equation we get; (1/2)v + v = 9 ; 1.5v = 9 Divide both sides by 1.5 v = 6 Now put this back into our first equation; u + v = 9 u + 6 = 9 Subtract 6 from both sides; u = 3 Now we synthesize this information; Final Answer: 53,611 Hope this helps! : ) *Edit* chin_hung148's answer is also correct; I just tried to make mine more easily interpreted by a younger person. - *Edit* To Brian D Your hypothesis about why the ten-thousands digit is 5 is incorrect. If a number is greater than 40,000 it could be 40,001. Also you should say that you edited your work when you do; you put in the wrong answer along with the wrong analysis at first. It makes people think that you are adjusting your answer based on theirs... : ) - *Edit* To Metallurgist Your analysis is incorrect; you did not read the question properly; I quote: 'My ones digit and ten digit are the same' So the answer is unique; 53,611 Hope this helps! : )

Answer 4

lets say the no. at unit's place is x and at the ten's place is y
so the number is actually 10y + x
Given that 10y + x = (x + y) + 9
so, y = 1
now if x = 2 then you can see that the sum of 1 +2 = 3 which is 9 less than 12
so ans is b)2

Answer 5

a + b = 10a + b - 9
a = 10a - 9
9a = 9
a = 1
1 + b = 10 + b - 9
b = b
b can be any digit 0 through 9

Answer 6

let x is in unit position and y in ten position .
then our required number is 10y+x.
According to question , 10y+x-9=x+y
oso, y=1 and x=0.
hence our requited no is 10.
proof: here sum of digits of our no is 1+0=1
10-1=9 proved.

Answer 7

d) 8.

The number is 18.

1 + 8 = 9

And 9 is 9 less than 18.

Answer 8

The answer would be 8.

Coz the number is 18.

Let 10s be x, let units be y

10x+y= x+y+9

9x+y=y+9

9x=9

meaning that x = 1

and the 'tens' is 1

Now, what is y?

We now that

10x+y= x+y+9

OK. I can't work it out.

Answer 9

WHAT explain me again
hit me baby one more time