Question 216536
The sum of two numbers is 92. One fifth of the first number added to one half of the second number is 34. Find the two numbers.


Step 1.  Let {{{x}}} be the first number and {{{92-x}}} be the second number.


Step 2.  Let {{{x/5}}} be one-fifth of the first number


Step 3.  Let {{{(92-x)/2}}} be one half of the second number.


Step 4.  Then, {{{x/5+(92-x)/2=34}}} since the first number added to one half of the second number is 34.


Step 5.  Solving yields the following steps.


Multiply 10 to both sides of the equation


{{{10*x/5+10*(92-x)/2=10*34}}}


{{{2x+5*(92-x)=340}}}


{{{460-3x=340}}}


Add 3x-340 to both sides of the equation


{{{460-3x+3x-340=340+3x-340}}}


{{{120=3x}}}


Divide 3 to both sides of the equation


{{{120/3=3x/3}}}


{{{x=40}}} and {{{92-x=52}}}


Check...{{{40/5+52/2=8+26=34}}}...which is a true statement


Step 6.  ANSWER:  The numbers are 40 and 52.


I hope the above steps were helpful.


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Good luck in your studies!


Respectfully,
Dr J