Question 77808: The difference between two positive integers is 52. One integer is three times as great as the other. Find the integers.
Answer by fetter6(6)   (Show Source):
You can put this solution on YOUR website! Let x and y represent the two integers and let us arbitrarily choose x>y. The first statement "the difference between two positive integers is 52" can then be written as an equation: x-y=52 (since x>y).
The second statement "one integer is 3 times as great as the other" must then be written as 3y=x (again, since x>y. If 3x=y this would imply that y>x, prove this to yourself!). So the two equations we have to work with are
1. x-y=52
2. 3y=x
Since 3y=x, we can substitute 3y for x in equation (1) to get 3y-y=52 => 2y=52 => y=26. Substitute this value of y=26 into equation (2) to get 3(26)=x => 78=x.
So the two positive integers are 78 and 26. QED
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