Respuesta :

mhanifa

Answer:

  • The original fraction is 4/7

Step-by-step 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
semsee45

Answer:

Original fraction = ⁴/₇

Step-by-step 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:

[tex]\implies \dfrac{x}{x+3}[/tex]

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

[tex]\implies \dfrac{2x}{x+3+14}=\dfrac{2}{3}\left(\dfrac{x}{x+3}\right)[/tex]

[tex]\implies \dfrac{2x}{x+17}=\dfrac{2x}{3(x+3)}[/tex]

[tex]\implies \dfrac{2x}{x+17}=\dfrac{2x}{3x+9}[/tex]

Cross multiply:

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

Divide both sides by 2x:

[tex]\implies 3x+9=x+17[/tex]

Subtract x from both sides:

[tex]\implies 2x+9=17[/tex]

Subtract 9 from both sides:

[tex]\implies 2x=8[/tex]

Divide both sides by 2:

[tex]\implies x=4[/tex]

Substitute the found value of x into the original fraction:

[tex]\implies \dfrac{4}{4+3}=\dfrac{4}{7}[/tex]

Therefore, the original fraction is ⁴/₇.

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