The denominator of a rational number is greater then its numerator by8.Numerator is increased by 17 & denomin?

Question

ator is decreased by 1, the number obtained is 3/2. Find the rational number.

Answer 1

Let the numerator be x.
Then the denominator is (x+8).
We are given that (x+17)/(x+8-1) = 3/2
Hence, (x+17)/(x+7) = 3/2

Now, let's multiply both sides by (x+7) to get:
(x+17) = (3/2)*(x+7)
And let's get rid of that 2 fraction by multiplying by 2:
2*(x+17) = 3*(x+7)
2x+34 = 3x+21
x = 13

The original numerator is 13, so the original denominator is 13+8 = 21.

The rational number is 13/21.

Answer 2

Let the numerator be x.
Then the denominator is (x+8).
We are given that (x+17)/(x+8-1) = 3/2
Hence, (x+17)/(x+7) = 3/2

Now, let's multiply both sides by (x+7) to get:
(x+17) = (3/2)*(x+7)
And let's get rid of that 2 fraction by multiplying by 2:
2*(x+17) = 3*(x+7)
2x+34 = 3x+21
x = 13

The original numerator is 13, so the original denominator is 13+8 = 21.

The rational number is 13/21.

Answer 3

Let the fraction be N/D where N is numerator and D is denominator.
From 1st statement D = N + 8
Therefore fraction is N /(N+8)
From IInd statement numerator of fraction is (N + 17) and Denominator became (D – 1) = (N + 8 ´– 1) = N +7
Therefore new fraction is (N + 17)/(N + 7)
From 2nd statement (N + 17)/(N + 7) = 3/2
or 2(N + 17) = 3(N+7)
or 2N + 34 = 3N + 21
or N = 13 & D = N + 8 = 13 + 8 = 21
Therefore fraction is 13/21

Answer 4

x = num
x + 8 = denom

(x + 17) / (x+8 - 1) = 3/2
(x+17) / (x+7) = 3/2
3(x+7) = 2(x+17)
3x + 21 = 2x + 34
x = 13
orig fraction = 13/21

Answer 5

Number is x/x+8.
(x+17)/(x+8-1)=3/2
(x+17)/(x+7)=3/2
3(x+7)=2(x+17)
3x+21=2x+34
x=13
so x/x+8
=13/(13+8)
=13/21

Answer 6

let d = the value of the denominator
n = the value of the numerator

d=n+8
(n+17)/(d-1)=3/2

Then,

n+17 3
_____ = ___

n+8-1 2

Cross multiply,

2(n+17)=3(n+7)
2n+34=3n+21
n=13

if n=13 and d=n+8,
d=13+8
d=21

So n/d = 13/21

Answer 7

13/21

Answer 8

13/21.

Answer 9

the number is 11\19