Posted by **Matthew** on Tuesday, August 28, 2012 at 9:39pm.

I have to figure out how to do this problem. I don't have the slightest idea how to even begin it, so if you can lead me through it, step by step, I would be very grateful.

A woman is walking home with eggs in her bag. Suddenly, a car comes speeding towards her. She jumps out of the way, just in time, as the car was going to hit her. Though the woman is unhurt, every eggs is broken. She goes back to the store, where she asks for a refund.

The manager comes to her, asking how many eggs she has. Though she doesn't know how many she has, she does know how she packaged them. When she tried to put the eggs in groups of two, there was one egg left over. The same thing happened when she put them in groups of three, four, five, and six. But, when she puts them in groups of seven, they all fit perfectly.

Your task is to answer the manager's question. What can you figure out from this information about how many eggs the farmer had? Is there more than one possibility?

- Math -
**Ms. Sue**, Tuesday, August 28, 2012 at 9:45pm
Look at multiples of 7. Which fit the criteria?

For instance,

14 doesn't work because it's divisible by 2.

21 doesn't work because in groups of 6, she'd have 3 left over.

Keep going.

- Math -
**Matthew**, Tuesday, August 28, 2012 at 9:49pm
That helps but I need a little more help than that...

- Math -
**Ms. Sue**, Tuesday, August 28, 2012 at 9:57pm
You can't possibly have listed the first 20 or so multiples of 7 in this short time!

- Math -
**Matthew**, Tuesday, August 28, 2012 at 10:08pm
Well, the thing is, the problem says that only one eggs is left over, but, four has three extra, and five has one extra... I'm throughally confused...

- Math -
**Matthew**, Tuesday, August 28, 2012 at 10:30pm
Can anyone help?

- Math -
**Matthew**, Tuesday, August 28, 2012 at 10:59pm
Oh, nevermind. Found it. The answer is 721 eggs...

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