The denominator of a fraction is three more than the numerator

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03-11-2022
Mathematics

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The denominator of a fraction is three more than the numerator

Sagot :

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DoloresU244979 DoloresU244979 · Answer 1 · 2022-11-03T08:23:27-04:00

Let it be x the numerator. Then we have:

• x + 3: Denominator.

,

• x + 9: Numerator increased by nine.

,

• (x + 3) + 9: Denominator increased by nine.

Since the simplified result of the fraction is 13/14, we can write and solve for x the following equation.

[tex]\begin{gathered} \frac{x+9}{(x+3)+9}=\frac{13}{14} \\ \frac{x+9}{x+3+9}=\frac{13}{14} \\ \frac{x+9}{x+12}=\frac{13}{14} \\ \text{ Apply cross product} \\ (x+9)\cdot14=13\cdot(x+12) \\ \text{ Apply distributive property} \\ 14\cdot x+9\cdot14=13\cdot x+13\cdot12 \\ 14x+126=13x+156 \\ \text{ Subtract 126 from both sides } \\ 14x=13x+156-126 \\ 14x=13x+30 \\ \text{ Subtract 13x from both sides} \\ 14x-13x=13x+30-13x \\ x=30 \end{gathered}[/tex]

Now, we replace the value of x into the left expression from the equation we just solved.

[tex]\begin{gathered} \text{ Original fraction }=\frac{x+9}{(x+3)+9} \\ \text{ Original fraction }=\frac{30+9}{30+3+9} \\ \text{ Original fraction }=\frac{39}{42} \end{gathered}[/tex]

Therefore, the original fraction is 39/42.

Sagot :

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