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 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
+128460
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
