Question 223809
If five times the smaller of two consecutive integers is added to three times the larger integer, the result is 59. Find both numbers.


Step 1.  Let n be one integer.


Step 2.  Let n+1 be the next consecutive integer.


Step 3.  Let 5n be five times the smaller integer.


Step 4.  Let 3(n+1) be three times the larger integer.


Step 5.  Then 5n+3(n+1)=59 since five times the smaller of two consecutive integers is added to three times the larger integer, the result is 59.


Step 6.  Solving the equation in Step 5 leads to the following steps:


*[invoke explain_simplification "5n+3(n+1)=59" ]


With n=7, then n+1=8.  Check sum... 5*7+3*8=35+24=59 which is a true statement.


Step 7.  The consecutive integers are 7 and 8.


I hope the above steps were helpful.


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Good luck in your studies!


Respectfully,
Dr J