+0  
 
0
157
1
avatar+11753 

a number consist of two digits whose sum is 9 .   9 is subtracted from the number  , the digits interchanged . find the number ?

rosala  May 24, 2014

Best Answer 

 #1
avatar+78719 
+5

OK, rosala, hang on for the ride!!

Let's call the first digit a and the second one b      .....    and   .....we know that

a + b = 9     (A)

So, let the larger number be written as

(10a + b)

And let the smaller number be wriiten as

(10b +a)

And their difference is 9  ...so...

(10a + b) - (10b + a) = 9     simplifying, we have

9a - 9b = 9       divide by  9

a - b = 1     (B)

So notice that we have two equations....(A) and (B)

a + b = 9

a - b =  1  

Let's just add them together to get rid of b

2a = 10     Divide by 2 on each side

a = 5    

And a + b = 9    so    5 + b = 9   So b =4

So the larger number = !0(5) + 4 = 54

And the smaller number = !0(4) + 5 = 45

And their difference is 9

CPhill  May 24, 2014
Sort: 

1+0 Answers

 #1
avatar+78719 
+5
Best Answer

OK, rosala, hang on for the ride!!

Let's call the first digit a and the second one b      .....    and   .....we know that

a + b = 9     (A)

So, let the larger number be written as

(10a + b)

And let the smaller number be wriiten as

(10b +a)

And their difference is 9  ...so...

(10a + b) - (10b + a) = 9     simplifying, we have

9a - 9b = 9       divide by  9

a - b = 1     (B)

So notice that we have two equations....(A) and (B)

a + b = 9

a - b =  1  

Let's just add them together to get rid of b

2a = 10     Divide by 2 on each side

a = 5    

And a + b = 9    so    5 + b = 9   So b =4

So the larger number = !0(5) + 4 = 54

And the smaller number = !0(4) + 5 = 45

And their difference is 9

CPhill  May 24, 2014

3 Online Users

avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details