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3 years ago

What value of x makes this proportion true? Α. 8 Β. 5 C. 105 D. 28

Mathematics

2 answers:

Elodia [21]3 years ago

8 0

I think that it wouldn’t be C

kompoz [17]3 years ago

3 0

8
because 3 x 5 = 15
8 x 5 = 40

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Marysya12 [62]

Let first consider the equations one by one and will be solving one by one ;

${:\implies \quad \sf x+\dfrac{1}{y}=4}$

Multiplying both sides by y will lead ;

${:\implies \quad \sf xy+1=4y}$

${:\implies \quad \boxed{\sf xy=4y-1\quad \cdots \cdots(i)}}$

Now, consider the second equation which is ;

${:\implies \quad \sf y+\dfrac{1}{x}=\dfrac14}$

Multiplying both sides by x will yield

${:\implies \quad \sf xy+1=\dfrac{x}{4}}$

${:\implies \quad \sf xy=\dfrac{x}{4}-1}$

${:\implies \quad \boxed{\sf xy=\dfrac{x-4}{4}\quad \cdots \cdots(ii)}}$

As LHS of both equations (i) and (ii) are same, so equating both will yield;

${:\implies \quad \sf 4y-1=\dfrac{x-4}{4}}$

Multiplying both sides by 4 will yield

${:\implies \quad \sf 16y-4=x-4}$

${:\implies \quad \sf 16y=x}$

Dividing both sides by y will yield :

${:\implies \quad \boxed{\bf{\dfrac{x}{y}=16}}}$

<em>Hence, the required answer is 16</em>

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