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



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ankur504
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x+(x+1)+(x+2)+(x+3)+(x+4)=75

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

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

*_Artist_*
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Yes...I understand....

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

*_Artist_*
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five

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

INewton
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Protip:
Use (x2) + (x1) + x + (x+1) + (x+2)

*_Artist_*
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4....

polpak
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4+3+2+1 is not 4.

*_Artist_*
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sorry...10

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

*_Artist_*
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umm...18?

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

polpak
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What do you do first?

*_Artist_*
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Umm....multiplication, 5*x?

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

polpak
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err by subtracting I mean.

*_Artist_*
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ooh...okay...duh

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

*_Artist_*
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13?

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

*_Artist_*
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39...

polpak
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no.

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

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

polpak
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Yes. Exactly.

polpak
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13 + 14 + 15 + 16 + 17 = 75

*_Artist_*
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Thank you...

polpak
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Of course! =)

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

polpak
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Not that it matters much, but sure ;p

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

INewton
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My method was cleaner *sad face*

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

polpak
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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.

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