Question 223553
The difference of two numbers is 12.  Two fifths of the greater number is six more than one third of the lesser number. Find both numbers


Step 1.  Let x be one smaller number


Step 2. Let y be the larger number.


Step 3.  Then -x+y=12 since the difference of two numbers is 12.


Step 4.  {{{2y/5=6+x/3}}} since two fifths of the greater number is six more than one third of the lesser number


Multiply by 15 to get rid of the denominators.


{{{15*2y/5=15*6+15x/3}}}


{{{6y=90+5x}}}


Subtract 5x from both sides of the equation


{{{-5x+6y=90}}}


Step 5.  So here's our system of linear equations  From Steps 3 and 4:


{{{-x+y=12}}}
{{{-5x+6y=90}}}


*[invoke linear_substitution "x", "y", -1, 1, 12, -5, 6, 90 ]


Step 6.  The numbers are 18 and 30.


I hope the above steps were helpful.


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Good luck in your studies!


Respectfully,
Dr J