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 a number and the reciprocal of
6 less than the number is 7 times the reciprocal of the
original number. Find the original number?

     Replace "a number", "the number", and "the original
number" all by the letter x.

     So we have:

The sum of the reciprocal of x and the reciprocal of 6 less
than x is 7 times the reciprocal of x.

     Now I'll do some blue coloring:

The sum of the reciprocal of x and the reciprocal of 6 less
than x is 7 times the reciprocal of x.

     Replace the blue words "the reciprocal of x" by "1/x":

The sum of 1/x and the reciprocal of 6 less than x is 7 times
1/x.

     Now I'll do some red coloring:

The sum of 1/x and the reciprocal of 6 less than x is 7
times 1/x.

     Replace "6 less than x" by "x-6" (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 x-6 is 7 times 1/x.

     Now I'll do some blue coloring:

The sum of 1/x and the reciprocal of x-6 is 7 times 1/x.

     Replace the blue words "7 times 1/x" by "7/x"

The sum of 1/x and the reciprocal of x-6 is 7/x.

     Now I'll do some red coloring:

The sum of 1/x and the reciprocal of x-6 is 7/x.

     Substitute the words "the reciprocal of x-6" by "1/(x-6)"

The sum of 1/x and 1/(x-6) is 7/x. 

     Now I'll do some blue coloring:

The sum of 1/x and 1/(x-6) is 7/x.

     Replace the words "The sum of 1/x and 1/(x-6)" by
"1/x + 1/(x-6)"

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

     Now I'll do some red coloring:

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

     Finally replace the word "is" by " = "

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