Question 32222
<pre><font size = 4><b>The sum of the reciprocal of a number and the reciprocal of 6
less than the number is 7 times the reciprocal of the
original number. Find the original number.

     Now I'll color parts of that sentence red:

The sum of the reciprocal of <font color = "red">a number</font> and the reciprocal of
6 less than <font color = "red">the number</font> is 7 times the reciprocal of <font color = "red">the
original number</font>. Find the original number?

     Replace "<font color = "red">a number</font>", "<font color = "red">the number</font>", and "<font color = "red">the original
number</font>" all by the letter <font color = "red">x</font>.

     So we have:

The sum of the reciprocal of <font color = "red">x</font> and the reciprocal of 6 less
than <font color = "red">x</font> is 7 times the reciprocal of <font color = "red">x</font>.

     Now I'll do some blue coloring:

The sum of <font color = "blue">the reciprocal of x</font> and the reciprocal of 6 less
than x is 7 times <font color = "blue">the reciprocal of x</font>.

     Replace the blue words "<font color = "blue">the reciprocal of x</font>" by "<font color = "blue">1/x</font>":

The sum of <font color = "blue">1/x</font> and the reciprocal of 6 less than x is 7 times
<font color = "blue">1/x</font>.

     Now I'll do some red coloring:

The sum of 1/x and the reciprocal of <font color = "red">6 less than x</font> is 7
times 1/x.

     Replace "<font color = "red">6 less than x</font>" by "<font color = "red">x-6</font>" (i.e., start with x and
then make it 6 less by subtracting 6 from it, getting x-6")

The sum of 1/x and the reciprocal of <font color = "red">x-6</font> is 7 times 1/x.

     Now I'll do some blue coloring:

The sum of 1/x and the reciprocal of x-6 is <font color = "blue">7 times 1/x</font>.

     Replace the blue words "<font color = "blue">7 times 1/x</font>" by "<font color = "blue">7/x</font>"

The sum of 1/x and the reciprocal of x-6 is <font color = "blue">7/x</font>.

     Now I'll do some red coloring:

The sum of 1/x and <font color = "red">the reciprocal of x-6</font> is 7/x.

     Substitute the words "<font color = "red">the reciprocal of x-6</font>" by "<font color = "red">1/(x-6)</font>"

The sum of 1/x and <font color = "red">1/(x-6)</font> is 7/x. 

     Now I'll do some blue coloring:

<font color = "blue">The sum of 1/x and 1/(x-6)</font> is 7/x.

     Replace the words "<font color = "blue">The sum of 1/x and 1/(x-6)</font>" by
"<font color = "blue">1/x + 1/(x-6)</font>"

<font color = "blue">1/x + 1/(x-6)</font> is 7/x

     Now I'll do some red coloring:

1/x + 1/(x-6) <font color = "red">is</font> 7/x

     Finally replace the word "<font color = "red">is</font>" by " <font color = "red">=</font> "

1/x + 1/(x-6) <font color = "red">=</font> 7/x

1/x + 1/(x-6) = 7/x

     Can you solve that? Hint: multiply thgrough by LCD = x(x-6) 

     If you can't solve that, post again.

Solution x = 36/5 or 7.2

Edwin McCravy
AnlytcPhil@aol.com</pre>