A fraction is equal to 5/9 when three is added to the numerator and to the denominator. Then when 5 is subtracted from numerator and denominator it is 1/5. Find the fraction
wardahd1234:
ok
Answers
Answered by
41
Let's assume the fraction to be =
Now, start doing the operations given.
Condition 1 : When 3 is added to the numerator and denominator ( The new fraction becomes = ), the fraction is equal to . In algebraic form :
=》 9x + 27 = 5y + 15
=》 9x + 27 - 15 = 5y
=》 y =
Condition 2 : When 5 is subtracted from the numerator and the denominator ( The new fraction becomes = ), the fraction is equal to . In algebraic form :
=》 5x - 25 = y - 5
=》 5x - 25 + 5 = y
=》 y = 5x - 20
We know that : y = y
=》 = 5x - 20
=》 9x + 12 = 25x - 100
=》 12 + 100 = 25x - 9x
=》 x =
=》 x = 7
y = 5 (7) - 20
=》 y = 15
Fraction becomes :
Answered by
26
Answer:
Step-by-step explanation:
Let the Original Fraction be x/y.
Case |,
( x+3) / (y+3) = 5 / 9.
=> 9 ( x +3) = 5 ( y+3)
=> 9x + 27 = 5y + 15
=> 9x - 5y = 15 - 27
=> 9x - 5y = -12 _____________(1).
Case || ,
( x-5 )/ ( y -5) = 1 / 5
=> 5 ( x-5) = y - 5
=> 5x - 25 = y - 5
=> 5x - y = 20
=> 5x - 20 = y _____________(2)
Putting y = 5x - 20 in eq (1).
=> 9x - 5 ( 5x - 20) = -12
=> 9x - 25 x + 100 = - 12
=> - 16 x = -112
=> x = 112 / 16
=> x = 7.
Putting x = 7 in eq (2). we get,
=> 35 - 20 = y
=> y = 15.
Hence,
The Original Fraction = x/y = 7 / 15.
Similar questions
Computer Science,
7 months ago
Biology,
7 months ago
Hindi,
7 months ago
History,
1 year ago
Physics,
1 year ago
Social Sciences,
1 year ago