a fraction becomes 9/ 11 if 2 is added to both the numerator and the denominator if 3 is added to both numerator and denominator it's become 5/6 find the fraction
Answers
Answered by
285
Let numerator be x and denominator be y.
If 2 is added to both numerator and denominator, the fraction becomes 9/11.
x+2/y+2 = 9/11
11(x+2) = 9(y+2)
11x+22 = 9y+18
9y-11x = 22-18
9y - 11x = 4
9y = 4+11x
y = (4+11x)/9
If 3 is added to both numerator and denominator, the fraction becomes 5/6.
x+3/y+3 = 5/6
6(x+3) = 5(y+3)
6x+18 = 5y+15
5y = 6x+18-15
5y = 6x+3
y = (6x+3)/5
(4+11x)/9 = (6x+3)/5
5(4+11x) = 9(6x+3)
20+55x = 54x + 27
55x-54x = 27-20
x = 7
y = (4+11(7))/9 = (4+77)/9 = 81/9 = 9
Therefore, x = 7 and y = 9
The fraction = 7/9
Hope it helps
If 2 is added to both numerator and denominator, the fraction becomes 9/11.
x+2/y+2 = 9/11
11(x+2) = 9(y+2)
11x+22 = 9y+18
9y-11x = 22-18
9y - 11x = 4
9y = 4+11x
y = (4+11x)/9
If 3 is added to both numerator and denominator, the fraction becomes 5/6.
x+3/y+3 = 5/6
6(x+3) = 5(y+3)
6x+18 = 5y+15
5y = 6x+18-15
5y = 6x+3
y = (6x+3)/5
(4+11x)/9 = (6x+3)/5
5(4+11x) = 9(6x+3)
20+55x = 54x + 27
55x-54x = 27-20
x = 7
y = (4+11(7))/9 = (4+77)/9 = 81/9 = 9
Therefore, x = 7 and y = 9
The fraction = 7/9
Hope it helps
Answered by
76
Answer:
Fraction = 7 / 9 .
Step-by-step explanation:
Let the numerator of fraction be x and denominator be y .
Friction = x / y
First case : [ When 2 added in both ]
x + 2 / y + 2 = 9 / 11
11 x + 22 = 9 y + 18
11 x - 9 y = - 4 ... ( i )
Second case : [ When 3 added in both ]
x + 3 / y + 3 = 5 / 6
6 x + 18 = 5 y + 15
6 x - 5 y = - 3 ... ( ii )
Now Multiply by 6 in ( i ) and by 11 in ( ii )
66 x - 54 y = - 24
66 x - 55 y = - 33
- + + [ Subtracting ( ii ) from ( i ) ]
y = 9
Now x = - 4 + 9 y / 11 ... ( i ) [ y = 9 ]
x = 77 / 11
= > 7
Now we have x = 7 and y = 9
Thus , fraction is 7 / 9 .
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