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The denominator of a fraction exceeds numerator by 3. If the numerator is doubled and the denominator is increased by 14, then fraction becomes 2/3rd of the original fraction.

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5 votes

Answer:

Original fraction = ⁴/₇

Explanation:

Numerator: top of the fraction

Denominator: bottom of a fraction

Let x be the original numerator.

If the denominator of a fraction exceeds the numerator by 3:


\implies (x)/(x+3)

If the numerator is doubled and the denominator is increased by 14, then fraction becomes 2/3rd of the original fraction:


\implies (2x)/(x+3+14)=(2)/(3)\left((x)/(x+3)\right)


\implies (2x)/(x+17)=(2x)/(3(x+3))


\implies (2x)/(x+17)=(2x)/(3x+9)

Cross multiply:


\implies 2x(3x+9)=2x(x+17)

Divide both sides by 2x:


\implies 3x+9=x+17

Subtract x from both sides:


\implies 2x+9=17

Subtract 9 from both sides:


\implies 2x=8

Divide both sides by 2:


\implies x=4

Substitute the found value of x into the original fraction:


\implies (4)/(4+3)=(4)/(7)

Therefore, the original fraction is ⁴/₇.

User Gabriel Belini
by
7.9k points
5 votes

Answer:

  • The original fraction is 4/7

Explanation:

Let the fraction be x/y.

According to question we have the following equations.

The denominator of a fraction exceeds numerator by 3:

  • y = x + 3

If the numerator is doubled and the denominator is increased by 14, then fraction becomes 2/3rd of the original fraction:

  • 2x/(y + 14) = (2/3)*(x/y)

Change the fraction as below and solve for y:

  • 2x /(y + 14) = 2x/(3y) Nominators are same
  • y + 14 = 3y Compare denominators
  • 2y = 14
  • y = 7

Find the value of x using the first equation:

  • 7 = x + 3
  • x = 7 - 3
  • x = 4

The fraction is:

  • x/y = 4/7
User Charles Desbiens
by
7.9k points

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