the denominator of a fraction is greater than its numerator by 9.if 7 is subtracted from both,its numerator and denominator, the fraction becomes 2/3.find the original fraction.
Answers
Answer:
Step-by-step explanation:
Let x=numerator,
y=denominator.
y=x+7 - - - - - (i)
(x+3)/(y+3) = 2/3
(Cross multiply)
3(x+3)=2(y+3)
3x+9=2y+6
(subtract 9 from both sides)
3x+9–9=2y+6–9
3x=2y+6–9
3x=2y-3 - - - - - - - (ii)
(substitute the value of equation (i) into (ii))
3x=2(x+7)-3
3x=2x+14–3
3x=2x+11
(subtract 2x from both sides)
3x-2x=2x+11–2x
x=11.
(substitute the value of x into equation (i))
y=7+11
y=18.
so numerator =11,
denominator = 18.
So original fraction is 11/18.
3/11th of original fraction is
= 11/18 x 3/11
= (11x3)/(18x11)
= 3/18
=1/6
Answer:
25/34
Step-by-step explanation:
let the numerator be x
so the denominator is x+9
ATQ
⇒x-7/x+9-7=2/3
⇒x-7/x+2=2/3
⇒3(x-7)=2(x+2)
⇒3x-21=2x+4
⇒3x-2x=4+21
∴x=25
so the numerator is 25 and denominator is 25+9=34
so the number is 25/34