Question 1137204: The sum of four times the first integer and five times the second interger is 77 find the intergers
Found 3 solutions by MathLover1, ikleyn, MathTherapy:
Answer by MathLover1(20850)   (Show Source):
Answer by ikleyn(52817)  (Show Source):
You can put this solution on YOUR website! .
The sum of four times the first  integer and five times the second integer is 77 find the integers
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Actually, this problem has INFINITELY MANY integer solutions, and there is NO WAY to select / (to identify) a UNIQUE solution.
The other tutor assumed, that the integers are consecutive integers, although the problem does not state it.
Obviously, this formulation missed one important condition and, therefore, is DEFECTIVE.
Answer by MathTherapy(10555)  (Show Source):
You can put this solution on YOUR website! The sum of four times the first integer and five times the second interger is 77 find the intergers
It BOGGLES my mind how some of these people come up with their solutions to these math problems. One of the sets of numbers JUST happens to be
consecutive, but where in this problem does it state that the numbers are CONSECUTIVE INTEGERS? Unless the person who responded erased that!
Why do these people continue to MISLEAD these people who ask for help?
The correct response: There are FOUR (4) sets of such numbers, as follows: 
By the way, these are the 4 POSITIVE values of the 2 numbers. If you see the sequence, the first increases by 5, and when it's increased by 5 to 23,
the second becomes a NEGATIVE INTEGER. In addition, if 5 is subtracted from the first, first number, 3, making it - 2, and you keep doing that,
the second takes on a set of POSITIVE INTEGERS. More is needed to determine exactly what 2 numbers are needed, so what I can say, for certain,
is that there are INFINITE SETS of these INTEGERS. It's also CLEAR that when the first increases by 5, the second DECREASES by 4.
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