the sum of the numerator and the denominator of a fraction is 4 more than twice the numerator. if 3 is added to each of the numerator and denominator, then their ratio becomes 2:3 . find the fraction.
Answers
Answer:
let the numerator be x
let the denominator be y
ATQ
- x+y=2x+4
x-2x+y=4
-x+y=4 --------1.
- x+3/y+3=2/3
3(x+3)=2(y+3)
3x+9=2y+6
3x-2y=6-9
3x-2y=3 -------2.
Multiply 1. by 3
-3x+3y=12 ------3
Add 2. and 3.
3x-2y=-3
+ -3x+3y=12
------------------------------
0+y=9
put y=9 in 1.
-x+9=4
x=9-4
x=5
fraction:5/9
let, the numerator be x
the denominator be y
therefore, the fraction : x/y
case - l:
x + y = 4 + 2x
x - 2x + y - 4 = 0
- x + y - 4=0 --------------------- (l) × 3
case - ll:
x + 3 /y + 3 = 2/3
3x + 9 = 2y + 6
3x - 2y + 9 - 6 = 0
3x - 2y + 3 = 0 -------------------- (ll) × 1
- 3x + 3y - 12 = 0
3x - 2y + 3 = 0
________________
y - 9 = 0
=> y = 9 -------------------- (lll)
putting (lll) in (l),
- x + 9 - 4 = 0
- x + 5 = 0
- x = - 5
x = 5
therefore, the fraction : 5/9
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