Question

The Numerator of a rational number is less than its denominator by 3 if the number become three times and the denominator is increased by 20 the new number becomes 1/8 find the original number.​

Answer 1

Step-by-step explanation:

I decide to make the numerator x and denominator x+3, preserving the relationship between their distance of 3, but making it so the numerator is a single term for solving simplicity.

x/(x+3) = original.

3x/(x+31) = 1/8 ⇒︎

24x = x+31 ⇒︎

23x = 28

we have an issue, your numberator and demoninator aren’t integers.

Let’s reconstruct your problem by changing the “3 less than” an the “multiply numerator by 3” and “add 8 to denominator” to be more arbitrary:

numerator y less than denominator, multiply by numerator by a, add b to denominator, and the result is z:

x/(x+y) = original,

ax/(x+y+b) = z

ax = z(x+b+y)

(a-z)x = (b+y)

x = (b+y)/(a-z)

For this problem to work (make sense) you need

(b+y)/(a-z) to be an integer and you need all four of those to be integers themselves

Answer 2

Answer:

Let the number of the rational number be x.

Then,the denominator of the rational number = x+3

According to the given condition,

New numerator = 3x and new denominator= (x+3) + 20=x+23

Given, 3x/x+23 = 1/8

By cross multiplying, we get

8 (3x) = x+23

= 24x = x+23

= 23x = x+23 ...... [On Transposing]

or x=1

Therefore, numerator of the rational number= 1

and denomirator = 1+3=4

Hence, the original rational number is 1/4.

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