Question

A housewife is travelling to market with all her eggs in one basket. She has between 100 and 200 eggs in the basket. Counting in threes there are 2 eggs leftover, counting in fives there is 1 egg leftover and counting in sevens there are 4 eggs leftover. How many eggs are in the basket?

Answer 1

x = 2 (MOD 3)
x=1 (MOD 5)
x=4 (MOD 7)

Answer 2

x=11 (MOD 15)
x=4 (MOD 7)

Answer 3

Can u solve for x?

Answer 4

x=11 (MOD 105)

Answer 5

So, x=105+11=116 eggs

Answer 6

Do u know MODULAR ARTHEMETIC.

Answer 7

@Lcoohill ???

Answer 8

cheers yes that is answer i got also thank you 11 mod 105
105 + 11 = 116

Answer 9

GREAT

Answer 10

Let eggs be the number of eggs.

Using Mathematica's constrained optimization function, Maximize:

Maximize
[
{eggs, Mod[eggs, 3] == 2, Mod[eggs, 5] == 1, Mod[eggs, 7] == 4, eggs >= 100, eggs <= 200},
{eggs},
Integers
]

{116, {eggs -> 116}}

http://reference.wolfram.com/mathematica/tutorial/ConstrainedOptimizationIntroduction.html