The sum of five consecutive integers is 75.
What is the third number? Please don't give me the answer right away....

- anonymous

- jamiebookeater

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- anonymous

x+(x+1)+(x+2)+(x+3)+(x+4)=75

- anonymous

yes...Can you help me figure out the answer?

- anonymous

Artist, do you see how he arrived at that equation?

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## More answers

- anonymous

Yes...I understand....

- anonymous

Ok, so how many x's do you have there on the left side.

- anonymous

five

- anonymous

Ok, so 5x. And what is the sum of the non-x's on the left side.

- anonymous

Protip:
Use (x-2) + (x-1) + x + (x+1) + (x+2)

- anonymous

4....

- anonymous

4+3+2+1 is not 4.

- anonymous

sorry...10

- anonymous

Ok, so the left side is 5x + 10 , and that equals 75. What is x?

- anonymous

umm...18?

- anonymous

No. What are the steps to solving
\[5x + 10 = 75\]

- anonymous

What do you do first?

- anonymous

Umm....multiplication, 5*x?

- anonymous

No. Isolate the x term, but subtracting 10 from both sides.

- anonymous

err by subtracting I mean.

- anonymous

ooh...okay...duh

- anonymous

Then divide both sides by 5 is the second step. What is x?

- anonymous

13?

- anonymous

Ok, so 13 is x is the first number, then what is the third number?

- anonymous

39...

- anonymous

no.

- anonymous

The sum of 5 sequential integers . The first integer is 13, what is the integer that comes after 13?

- anonymous

Duh,14...so the third number is 15?

- anonymous

Yes. Exactly.

- anonymous

13 + 14 + 15 + 16 + 17 = 75

- anonymous

Thank you...

- anonymous

Of course! =)

- anonymous

I fanned you! Can you fan me? you'll be my tenth fan!

- anonymous

Not that it matters much, but sure ;p

- anonymous

Thanks...It's kinda neat to have ten fans...

- anonymous

My method was cleaner *sad face*

- anonymous

Ooh...sorry....*sympathetic face*

- anonymous

I agree Newton, but ankur had already started in this vein, and it doesn't matter much either way, so long as the method is understood.

- anonymous

Yes...I agree...Maybe next time INewton....

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