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the denominator of a fraction is 3 more than the numerator. if both the numerator and denominator are increased by 4, the new fraction is equal to 3/4. what is the original fraction

Sagot :

Explanations:

Let the numerator of the fraction be x and let the denominator be y.

Hence, the original fraction is:

[tex]\frac{x}{y}[/tex]

It is given that the denominator is 3 more than the numerator. It follows that:

[tex]y=x+3[/tex]

It is also given that when both the numerator and denominator are increased by 4, the new fraction is equal to 3/4. This implies mathematically to the equation:

[tex]\frac{x+4}{y+4}=\frac{3}{4}[/tex]

Simplify this equation:

[tex]\begin{gathered} 4(x+4)=3(y+4) \\ \Rightarrow4x+16=3y+12 \end{gathered}[/tex]

Substitute y=x+3 into this equation:

[tex]4x+16=3(x+3)+12[/tex]

Solve the equation for x:

[tex]\begin{gathered} \Rightarrow4x+16=3x+9+12 \\ Collect\text{ like terms:} \\ \Rightarrow4x-3x=9+12-16 \\ \Rightarrow x=5 \end{gathered}[/tex]

Substitute x=5 into the equation y=x+3:

[tex]y=5+3=8[/tex]

Hence, x=5, and y=8.

It follows that the original fraction is 5/8.

Answer:

The original fraction is 5/8.

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