Question 228836
The sum of three numbers is 123.  The second number is 9 less than two times the first number.  The third number is 6 more than three times the first number. Find the three numbers.  Thank you very much.


Step 1.  Let n be the first number.


Step 2.  Let 2n-9 be the second number since it is 9 less than two times the first number.


Step 3.  Let 3n+6 be the third number since it is 6 more than three times the first number.


Step 4.  Then n+2n-9+3n+6=123 since their sum is 123.


Step 5.  Solving n+2n-9+3n+6=123 yields the following steps


{{{6n-3=123}}}


Add 3 to both sides of the equation


{{{6n-3+3=123+3]]]


{{{6n=126}}}


Divide by 6 to both sides of equation


{{{6n/6=126/6}}}


{{{n=21}}} {{{2n-9=42-9=33}}}  and {{{3n+6=63+6=69}}}.


Note the above numbers should add up to 123:  21+33+69=123...which it does.


Step 6.  ANSWER:  The numbers are 21,33, and 69.


I hope the above steps were helpful.


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Good luck in your studies!


Respectfully,
Dr J