Question 893959
The product of two positive numbers is 9. The reciprocal of one of these numbers is 4 times the reciprocal of the other number. What is the sum of the two numbers?
<pre>
Let the smaller number be S
Then larger number = {{{9/S}}}
When the numbers become reciprocals, the smaller number becomes the LARGER reciprocal, and the
larger number becomes the SMALLER reciprocal
Thus, the larger reciprocal is: {{{1/S}}}, and the smaller reciprocal is: {{{1/(9/S)}}}, or {{{S/9}}}
Therefore, the LARGER RECIPROCAL, equals 4 times the SMALLER RECIPROCAL, OR
{{{1/S = 4(S/9)}}}
{{{1/S = 4S/9}}}
{{{4S^2 = 9}}} ------- Cross-multiplying
{{{S^2 = 9/4}}}
S, or smaller number = {{{sqrt(9/4)}}}, or {{{highlight_green(3/2)}}}
Larger number: {{{9/(3/2)}}}, or {{{9(2/3)}}}, or {{{highlight_green(6)}}}

Sum of the two numbers: {{{3/2 + 6}}}, or {{{3/2 + 12/2}}}, or {{{15/2}}}, or {{{highlight_green(15/2)}}}, or {{{highlight_green(7.5)}}}
You can do the check!! 

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