Monday

October 20, 2014

October 20, 2014

Posted by **Susan** on Monday, November 29, 2010 at 11:30am.

Every third pumpkin had no stem.

Every sixth pumpkin was too small.

Every fourth pumpkin was too big.

Every fifth pumpkin was not perfectly round.

How many perfect pumpkins were in Farmer Frank's pumpkin patch?

Only algebraic solutions will be accepted.

- math -
**Henry**, Tuesday, November 30, 2010 at 12:10pmBad Pumpkins = (1/3 + 1/6 + 1/4 + 1/5)360 = ((20 + 10 + 15 + 12) / 60)360 = (57/60)360 =(19/20)360 = 342.

Perfect P umpkins = 360 - 342 = 18.

- math -
**Steve**, Friday, November 23, 2012 at 11:20amThat can't be right. At least all the prime-numbered pumpkins are perfect, and there are than 70 primes less than 360 (excluding 3 and 5).

I think you just didn't carry through the procedure far enough. If you scratch out all the 1/3 and 1/4, you have counted 1/12 twice, so you need to add it back in. Same for other pairs of factors.

360

-360(1/3 + 1/4 + 1/5 + 1/6)

+360(1/12 + 1/15 + 1/18 + 1/20 + 1/24 + 1/30)

-360(1/60 + 1/72 + 1/120)

+360(1/360)

= 124

But that doesn't count #1, which isn't one of the multiples. So, I think

125 is the final count.

**Answer this Question**

**Related Questions**

math - there were 360 pumpkins in a pumpkin patch , but it was difficult for ...

logic - There were 1320 pumpkins in a pumpkin patch, but it was difficult for ...

math logic - There were 1320 pumpkins in a pumpkin patch, but it was difficult ...

math logic - There were 1320 pumpkins in a pumpkin patch, but it was difficult ...

math - went to market with a whole crop of pumpkins which I had grown in my ...

Physics - Early one October you go to a pumpkin patch to select your Halloween ...

Physics - Early one October, you go to a pumpkin patch to select your Halloween ...

Algebra 2 - The Pumpkin Patch Doll Company has detrmined that the profit the ...

chemistry: brain teaser - I have this question that i am having trouble with.....

Math - The size to which a pumpkin grows while on the vine is probably ...