The sum of three consecutive integers is 42. Find the Integers.
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OpenStudy (anonymous):
x+(x+1)+(x+2)=42??????
OpenStudy (anonymous):
does that look right to anyone?
OpenStudy (isaiah.feynman):
Yes that is absolutely right!!!
OpenStudy (anonymous):
it's nicer IMHO to label the middle \(n\) and so that our three are \(n-1,n,n+1\) -- when you sum them they cancel out nicely
OpenStudy (anonymous):
Isaiah will you please help me with this?
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OpenStudy (anonymous):
ok so its x+(x+1)+(x+2)=42
OpenStudy (isaiah.feynman):
Yes, I've solved and verified. You are right!!! Simply solve for x
OpenStudy (anonymous):
I'm trying to remember how to do this
OpenStudy (anonymous):
hmmm
OpenStudy (isaiah.feynman):
When you sum them up it becomes 3x+3=42. Solve for x...
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OpenStudy (anonymous):
3x+3=42??
OpenStudy (anonymous):
ok wow that took forever
OpenStudy (isaiah.feynman):
lol
OpenStudy (anonymous):
x=13 got it thanks
OpenStudy (anonymous):
If I didn't need to pass this class I would of left that problem a long time ago
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OpenStudy (anonymous):
its not adding up to 42
OpenStudy (isaiah.feynman):
Try again :)
OpenStudy (anonymous):
alternatively, we have \(n-1,n,n+1\) our three consecutive integers and their sum is:$$(n-1)+n+(n+1)=42\\3n=42\\n=\frac{42}3=\frac{2\times21}3=2\times7=14$$hence our integers are \(13,14,15\). they do indeed sum to \(42\)