SOLUTION: THIS WAS GIVIN TO ME BY MY TEACHER, AND IT'S JUST GOT ME STUMPED COMPLETELY. Clue 1: Safe combination... 15-22-?-5-38 Clue 2: Start with three consecutive integers between

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Question 335536: THIS WAS GIVIN TO ME BY MY TEACHER, AND IT'S JUST GOT ME STUMPED COMPLETELY.
Clue 1:
Safe combination...
15-22-?-5-38
Clue 2:
Start with three consecutive integers between -10 and 10. twice the third is 13 greater than 3x the sum the first and the second.
Clue 3:
If you ever find those integers, multipy them together then divide them by -2.
Can you figure out the combination?
-Alexis Stephenson, Thank You.
Found 2 solutions by jim_thompson5910, solver91311:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Since it states that we should "Start with three consecutive integers between -10 and 10. twice the third is 13 greater than 3x the sum the first and the second", this means that 2%28x%2B2%29=3%28x%2Bx%2B1%29%2B13 where 'x', 'x+1', and 'x+2' are the consecutive numbers.


2%28x%2B2%29=3%28x%2Bx%2B1%29%2B13 Start with the given equation.


2x%2B4=3x%2B3x%2B3%2B13 Distribute.


2x%2B4=6x%2B16 Combine like terms on the right side.


2x=6x%2B16-4 Subtract 4 from both sides.


2x-6x=16-4 Subtract 6x from both sides.


-4x=16-4 Combine like terms on the left side.


-4x=12 Combine like terms on the right side.


x=%2812%29%2F%28-4%29 Divide both sides by -4 to isolate x.


x=-3 Reduce.


Since x=-3, the three consecutive numbers are: -3, -2, -1


Multiply them out to get: (-3)*(-2)*(-1)=-6


Then divide that by -2 to get (-6)/(-2)=3


So the missing number is 3.

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Let represent the least of the three consecutive integers. The second one is then and the next one is

Twice the third:

Three times the sum of the first and third plus 13:

So



Solve for , calculate the other two integers by adding 1 and then adding 1 again. Multiply the three together, then divide by -2. Let me know how you did.

John

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