Problem Statement: (Write the problem in your own words with enough detail that an absent classmate could understand the problem.)

Question

A farmer is taking her eggs to market in her cart. Along the way, she hits a pothole, which jars her cart and spills the eggs. Though the farmer is unhurt, every single egg is broken. She goes to her insurance agent, who asks her how many eggs she had. She doesn’t remember, but she does remember some things from the ways she tried packing the eggs.

Here is what she remembers:

1. When she put the eggs in groups of two, there was one left over.
2. When she put the eggs in groups of three, there was also one egg left over.
3. When she put the eggs in groups of four, groups of five, and groups of six, there was also just one egg left over.
4. When she put the eggs in groups of seven, she ended up with complete groups of seven, with no eggs left over.

Answer 1

43x7 = 301

301/2 = 150 + 1 egg

301/3 =100 + 1

301/4 = 75 + 1

301/5 = 60 + 1

301/6 = 50 + 1

301/7 = 43 + 0

301 is the minimum number of eggs that satisfy the conditions

such as 1141 = 163x7

1141/2= 570 with one egg left over

same with

1141/3 = 380 and one egg

1141/4 = 285 and one egg

1141/5= 228 and one egg

1141/6 = 190 and one egg

while

111417 = 163

there may be an infinite number of other solutions

at some point those solutions may be physically impossible

A cart can only carry so many eggs

Plus that insurance company will minimize any payment and go with the lowest number possible.

and that's probably all the insurance will pay for: 301 or 1141 if they can

although there are more possibilities, all will be a prime number times 7

If she missed her last insurance premium she gets nothing.