SOLUTION: the difference between two positive integers is 40. one integer is three times as great as the other. find the integers

Question 656002: the difference between two positive integers is 40. one integer is three times as great as the other. find the integers
Answer by DrBeeee(684) (Show Source): You can put this solution on YOUR website!
Let n = one of the positive integers (or just one of the numbers, it doesn't matter what you call it)
Let m = the other number
By the problem statement we have
(1) m = 3*n and
(2) m - n = 40
Substitute m of (1) into (2) and get
(3) 3*n - n = 40 or
(4) 2*n = 40 or
(5) n = 20
Using (2) we get
(6) m - 20 = 40 or
(7) m = 60
Use (1) to check your answer,
Is (60 = 3*20)?
Is (60 = 60)? Yes
Answer: The two numbers (positive integers) are 20 and 60.
Note that the answer is two positive integers, simply because of the use of integers 3 and 40 in the problem statement. Arithmetically, we had no "control" over this result, therefore the problem to find "two positive integers" has no bearing on the solution to the problem, it merely adds confusion to the beginning algebra student.
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