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**+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

#1**+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