Question 221523
Determine whether there are two consecutive odd integers such that 5 times the first exceeds 3 times the second by 54.


Step 1.  Let n be the first odd integer.


Step 2.  Let n+2 be then next consecutive odd integer.


Step 3.  Let 5n be 5 times the first odd integer.


Step 4.  Let 3(n+2) be 3 times the second odd integer.


Step 5. Then,  5n=3(n+2)+54 since 5 times the first exceeds 3 times the second by 54


Step 6.  Solving the equation in Step 5 yields the following steps:


{{{5n=3(n+2)+54}}}


{{{5n=3n+6+54}}}


{{{5n=3n+60}}}


Subtract 3n from both sides of the equation


{{{5n-3n=3n+60-3n}}}


{{{2n=60}}}


Divide by 2 to both sides of the equation yields


{{{2n/2=60/2}}}


{{{n=30}}}  but n is an even integer.  


Step 8.  ANSWER:  Therefore there are no odd integers that satisfies the given problem statement.


I hope the above steps were helpful.


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Good luck in your studies!


Respectfully,
Dr J