Question 140018
a) 

Let x=first number and y=second number

b) 

Since "One number exceeds another by 5", this means that the first equation is {{{y=x+5}}}

c) 

The product of the two numbers in terms of x is 

{{{x(x+5)=x^2+5x}}}


d) 

The value of x is 7



----------------------------



So let's solve the problem



Let x=first number and y=second number


Since "One number exceeds another by 5", this means that the first equation is {{{y=x+5}}}


Also, because "The sum of their reciprocals equal to 19 divided by the product of the two numbers" we have the second equation


{{{1/x+1/y=19/(x*y)}}}


{{{1/x+1/(x+5)=19/(x*(x+5))}}} Plug in {{{y=x+5}}}



{{{(x*(x+5))(1/x+1/(x+5))=(x*(x+5))(19/(x*(x+5)))}}} Multiply both sides by the LCD {{{x*(x+5)}}} to clear out the fractions



{{{x+5+x=19}}} Distribute and multiply 



{{{2x+5=19}}} Combine like terms on the left side



{{{2x=19-5}}}Subtract 5 from both sides



{{{2x=14}}} Combine like terms on the right side



{{{x=(14)/(2)}}} Divide both sides by 2 to isolate x



{{{x=7}}} Divide


--------------------------------------------------------------

Answer:

So our answer is {{{x=7}}}