The numerator of a fraction is 6 less than the denominator.If 3 is added to the numerator,the fraction becomes equal to 2/3.Fin the original fraction.
2007-01-17 02:34:51 · 8 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
(x-1/3)4 = 28
x-1/3 = 7
x = 7+1/3 = 22/3
original fraction is (x-6)/x
((x-6)+3)/x = 2/3
(x-3)/x = 2/3
3(x-3) = 2x
3x-9 = 2x
x = 9
So original fraction is 3/9 = 1/3
2007-01-17 02:37:33 · answer #1 · answered by catarthur 6 · 1⤊ 0⤋
Just translate the words into equations. If the numerator is 6 less than the denominator, then the fraction is (x-6)/x for some number "x". You're told that if you add 3 to the numerator, the fraction is equal to 2/3. So: (x-6 + 3)/x = 2/3.
Multiply both sides of this by x and you get:
(x - 6 + 3) = 2x/3
Add the 3 to the -6, multiply both sides by 3, etc. and solve for x:
(x - 3) = 2x/3
3*(x - 3) = 2x
3x - 9 = 2x
3x - 2x - 9 = 0
x - 9 = 0
x = 9
The original question though was to find the fraction. We said it was in the form of (x-6)/x. So plug in x-9, and you get "3/9". This is the answer. DO NOT reduce the fraction to 1/3, because although that's the normal convention, "1/3" doesn't describe the original fraction we're looking for (where the numerator is 6 less than the denominator). Again, the FRACTION we want is "3/9".
2007-01-17 02:48:54 · answer #2 · answered by Anonymous · 1⤊ 0⤋
By condition
(x-1/3)4=28
x=22/3
Let the fraction be x-6/x
(x-6+3)/x=2/3
x=9
So the fraction =3/9=1/3
2007-01-17 03:29:13 · answer #3 · answered by navin p 2 · 0⤊ 0⤋
1) (a-1/3)4 = 28
a- 1/3 = 28/4 = 7
a= 7+1/3
a= (21 +1)/3
a= 22/3 = 7.333
2) (a-6)/a and (3 + (a-6))/ a= 2/3
Let's calculat the 2nd equation to find a:
(3+a-6)/a = 2/3
(a - 3)/a = 2/3
1 - 3/a = 2/3
1 -2/3 = 3/a
1/3 = 3/a
a = 9
we can replace a=9 in the first equation:
(a-6)/a = (9-6)/9 = 3/9 = 1/3
The equation is equal to 1/3
2007-01-17 02:48:18 · answer #4 · answered by loulou 2 · 0⤊ 0⤋
a) (x-1/3)*4=28 ==> x-1/3= 7==>x= 22/3
b) (d-6)/d is the original fraction (d-3)/d =2/3==> 2d =3d-9==>
d=9
The original fraction is 3/9=1/3
2007-01-17 03:53:08 · answer #5 · answered by santmann2002 7 · 0⤊ 0⤋
Answer to first question: 22/3
Answer to second question: 1/3
2007-01-17 09:47:21 · answer #6 · answered by Anonymous · 0⤊ 0⤋
enable x be the decision you idea after we multiply it by 8 , the decision is 8x and subtract it with sixty six then effect is two times the decision you idea i.e.2x, 8x-sixty six=2x , 8x-2x=sixty six, 6x=sixty six, x=sixty six/6=11 x= 11
2016-11-24 23:09:05 · answer #7 · answered by ? 4 · 0⤊ 0⤋
1)X-1/3=Y
4Y=28
Y=7
3X-1=21
3X=22
X=22/3
2)OF=X/Y
X=Y-6
(Y-6+3)/Y=2/3
(Y-3)/Y=2/3
3Y-9=2Y
Y=9
X=3
OF=X/Y=3/9=1/3
2007-01-17 06:15:22 · answer #8 · answered by ARUN 1 · 0⤊ 0⤋