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# clear and easy explaination

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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

#1
+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
+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

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