Question 763030: the sum of the digits of a three-place number is 19. If the tens and units digits are interchange the number is diminished by 27, and if the hundreds and ten digits are interchange the number is increased by 180. What is the number?
Answer by ramkikk66(644)   (Show Source):
You can put this solution on YOUR website! Though this looks complicated, it isn't and can be solved through linear equations.
Step 1:
Let the digit in 10's place be x and digit in unit's place be y.
Then digit's in 100's place = 19 - (x+y) = 19 - x - y (since sum of the 3 digits is 19)
Step 2:
Value of the original number =  = 
Step 3:
If 10's and unit's places are interchanged, 10's place becomes y and units place is x. 100's place is still 19-x-y.
The value of the new number is
 = 
Given that this is less than the original number by 27, we get the equation
Simplifying, we get  or  Eqn (1)
Step 4:
If 100's and 10's places are interchanged, x comes to the 100's place and (19-x-y) comes to the 10's place. Units place is stilly.
The value of this new number is
 = 
Given that this is 180 more than the original number, we get the equation
Simplifying, we get:  or  Eqn (2)
Step 5:
We can solve Eqn(1) and (2) to get x and y
Add eqns(2) and (1) to get  or 
Since x - y = 3, 
Hence 100'th place = 
The original number = 
Check your answer:
Swapping 10's and units, we get 658, and 685 - 658 = 27
Swapping 100's and tens, we get 865, and 865 = 685 + 180.
Got it?
:)
|
|
|
