SOLUTION: The sum of two positive integers is a maximum of 20. The larger integer is 8 more than 3 times the smaller integer.Determine the possible values for the larger integer?

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Question 887278: The sum of two positive integers is a maximum of 20. The larger integer is 8 more than 3 times the smaller integer.Determine the possible values for the larger integer?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
x + y <= 20
y = 3x + 8
replace y with 3x + 8 in the first equation to get x + 3x + 8 <= 20
simplify to get 4x + 8 <= 20
subtract 8 from both sides of this equation to get 4x <= 12
divide both sides of this equation by 4 to get x <= 3
the smaller number is less than or equal to 3
the possible values for the smaller number are 1,2,3
when x = 1,2,3, y would take on the following values:
         x         y = 3x + 8         sum of x and y

         1             11                  12
         2             14                  16
         3             17                  20

the possible values for the larger integer are 11, 14, 17.