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Write and solve equations here.  Let the two numbers be x and y.  

Then x + 3y = 24, and 5x + 3y = 36.  Solve this system of linear equations.

Note that the first equation can easily be solved for x.  Then x = 24 - 3y.  Subbing 24 - 3y for x in the 2nd eq'n, we get:

5(24 - 3y) + 3y = 36, or   120 - 15y + 3y = 36

                                                    -12y     = 36 - 120, or -12y = -84
                                                                                     -84
                                                       Solving for y:  y = = 7
                                                                                      -12

If y is 7, then x is 24 - 3(7).  Simplifying, x = 24 - 21 = 3.

Then the solution is (3, 7).

By all means insert 3 for x and 7 for y in either of the original equations.  If that equation comes out to be true, you'll know your solution is correct.