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# One number is 4 times another number. If the sum of their reciprocal is equal to 5/12, find the two numbers

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1787
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One number is 4 times another number. If the sum of their reciprocal is equal to 5/12, find the two numbers

Feb 28, 2015

#4
+27342
+5

Hmm!  Your first expression isn't right either Nauseated.

$$\\ \frac{1}{x}+\frac{1}{4x}=\frac{5}{12}\\\\\frac{4}{4x}+\frac{1}{4x}=\frac{5}{12}\\\\\frac{5}{4x}=\frac{5}{12}\\\\4x=12\\\\x=3$$

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Feb 28, 2015

#1
+94526
+5

Let x be the first number and 4x the second.

So we have

x + 1/(4x)= 5/12    mutiply both sides by 4x

4x^2 + 1 = (20/12)x

4x^2 + 1 = (5/3)x    multiply both sides by 3

12x^2 + 3 = 5x      rearrange

12x^2 - 5x + 3 = 0

This doesn't have a real solution......????

Feb 28, 2015
#2
0

Sorry but the guy above me is incorrect. The answer is actually x=1.5 thankyou very much and goodnight. Now I can have the cool shades on

Feb 28, 2015
#3
+1036
0

Well, Anon, maybe you should take off the blinders instead of putting more on. But I guess this is normal for you because you are a m***n. Too bad there isn’t a “close pin on the nose” emoto. One reason for the nausea of CDD is the stench. Morons with CDD are very foul!

$$\Text {solution :} \\\\ \hspace*{1em} \dfrac{1}{x}+\dfrac{1}{(x+4)}\;= \; \dfrac{5}{12} \hspace*{3em} \Leftarrow \; \text {Solve} \\\\ \hspace*{1em} 12(x+4)+12x=5x(x+4)\hspace{10pt} \Leftarrow \; \text {simplify using 12x(x+4) } \\\ \hspace*{3em} 24x+48=5x^2+20x \hspace{16pt} \Leftarrow \; \text {expand } \\ \hspace*{3em} -5x^2+4x+48=0 \hspace*{1em} \; \Leftarrow \ {Subtract}\; 5x^2+20x \; \text {and set = 0}\\\\ x = \dfrac{-(4)\pm \sqrt{((4^2)-4 \times(-5)(48))}}{2(-5)} \hspace*{1em} \Leftarrow \; \text { Use quadratic formula}\\\\\\\\$$

$$\text {. .}\ \\\ \hspace{1pt} \qquad -4 \pm \dfrac {\sqrt{976}}{-10}}\\\\ \hspace{1pt} \qquad \text {x = -2.7240998703626618} \\\ OR \\ \hspace{34pt}\text {x = 3.5240998703626616} \\$$

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Feb 28, 2015
#4
+27342
+5

Hmm!  Your first expression isn't right either Nauseated.

$$\\ \frac{1}{x}+\frac{1}{4x}=\frac{5}{12}\\\\\frac{4}{4x}+\frac{1}{4x}=\frac{5}{12}\\\\\frac{5}{4x}=\frac{5}{12}\\\\4x=12\\\\x=3$$

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Alan Feb 28, 2015
#5
+95177
0

Thanks Alan,

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My goodness Nauseated, it seems you have become contaminated very badly with CDD.

You must be hospialised and quarantined immediately.

Do not fret the nurses wear face masks and nose pins so that they can handle the stench!

Plus it is their calling so they shall nurse you back o health while they struggle to control their nausea.

Feb 28, 2015
#6
+1036
0

OH,OH Revenge is in the shadows! HAHAHA!

I wondered why this was so complicated. Most of the time I can figure the answer just by looking. Along with the clothespin, a pair of untinted spectacles might help.

Well, CPhill, it looks like we have the same strain of CDD.

Thanks Alan!

Feb 28, 2015