SOLUTION: Five less than six times the largest of three consecutive positive integers is equal to the square of the smallest integer minus two times the middle integer. Find the largest inte

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Five less than six times the largest of three consecutive positive integers is equal to the square of the smallest integer minus two times the middle integer. Find the largest inte      Log On


   

Question 1142962: Five less than six times the largest of three consecutive positive integers is equal to the square of the smallest integer minus two times the middle integer. Find the largest integer.
Found 3 solutions by josgarithmetic, solver91311, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
system%28n-2%2Cn-1%2Cn%29
Ambiguous Interpretation - the wrong one
highlight_green%286n-5=%28n-2%29%5E2-2%28n-1%29%29
6n-5=n%5E2-4n%2B4-2n%2B2
n%5E2-4n-2n-6n%2B2%2B5=0
n%5E2-12n%2B7=0
%28n-3%29%28n-4%29=0
n=4

--
2,3,4 the consecutive positive integers.
check:
6%2A4-5=%284-2%29%5E2-2%284-1%29
19=4-4=0
FALSE

--
Different Interpretation -the right one
6n-5=%28n-2-2%28n-1%29%29%5E2
-
6n-5=%28n-2-2n%2B2%29%5E2
6n-5=%28-n%29%5E2
6n-5=n%5E2
n%5E2-6n%2B5=0
%28n-1%29%28n-5%29=0
highlight%28n=5%29
-
check:
6%2A5-5=%285-2-2%285-1%29%29%5E2
25=%283-2%2A4%29%5E2
25=%28-5%29%5E2, okay
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Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Let represent the largest of the three integers, then the next smaller one would be , and the next smaller would be .

Six times the largest: . Five less than six times the largest: . The square of the smallest: . Two times the middle one: .



So



Solve for . Discard the smaller of the two roots (1) because if one is the largest of three integers they can't all be positive.


John

My calculator said it, I believe it, that settles it

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Five less than six times the largest of three consecutive positive integers is equal to the square of the smallest integer minus two times the middle integer. Find the largest integer.
The other person is TOTALLY CONFUSED, as always!! 

Thus, MOST of what he mentions in his "stab" at a solution makes NO SENSE, whatsoever.

Is this problem open to different interpretations? I think NOT!!

Having said this, the CORRECT ANSWER IS: highlight_green%28matrix%281%2C3%2C+Largest%2C+%22INTEGER%3A%22%2C+11%29%29