the sum of the digits of a two digit number is 9. the fractions formed by taking 9 less than the no.. as numerator and 9 more than the number as denominator is 3/4. what is the number

Guest Aug 18, 2017

#1**+1 **

Let the number = a, then:

(a-9) / (a+9)=3/4

Solve for a:

(a - 9)/(a + 9) = 3/4

Cross multiply:

4 (a - 9) = 3 (a + 9)

Expand out terms of the left hand side:

4 a - 36 = 3 (a + 9)

Expand out terms of the right hand side:

4 a - 36 = 3 a + 27

Subtract 3 a - 36 from both sides:

**Answer: | a = 63**

Guest Aug 18, 2017

#2**+1 **

The sum of the digits of a two digit number is 9. the fractions formed by taking 9 less than the no.. as numerator and 9 more than the number as denominator is 3/4. what is the number

Let the digits be a and b

Note that we can write any two-digit number as 10a + b

So we have this system

a + b = 9

[ (10a + b) - 9] / [ (10a + b) + 9] = 3/4

Manipulating the first equation, we have that b = 9 - a

Subbing this into the second equation, we have that

[ (10a + 9 - a) - 9] / [ (10a + 9 - a) + 9 ] = 3/4 simplify

[ 9a] / [ 9a + 18] = 3/4 cross-multiply

4[9a] = 3 [9a + 18 ] simplify

36a = 27a + 54 subtract 27a from both sides

9a = 54 divide both sides by 9

6 = a

And b = 9 - a = 9 - 6 = 3

So....our number is 63

Proof that this is correct :

[63 - 9] / [63 + 9 ] = 54 / 72 = [3 * 18 ] / [ 4 * 18 ] = 3 / 4

CPhill
Aug 18, 2017