Hardest question in the world! If solved huge surprise

Once upon a time, an old lady want to sell her eggs at the local market.
When asked how many she had she replied I can’t count past 100 but I know that:

If you divide the number of eggs by two there will be one egg left.
If you divide the number of eggs by three there will be one egg left.
If you divide the number of eggs by four there will be one egg left.
If you divide the number of eggs by five that will be one egg left.
If you divide the number of eggs by six there will be one eggs left.
If you divide the number of eggs by someone there will be one egg left.
If you divide the number of eggs by eight there will be one egg left.
If you divide the number of eggs by nine there will be one egg left.
If you divide the number of eggs by 10 that will be one egg left.
If you divide the number of eggs by 11 that will be no eggs left
how many eggs did the Lady have

9514 1404 393

  25201

Step-by-step explanation:

The number of eggs is one more than some factor times the LCM of 2, 3, 4, 5, 6, 7, 8, 9, and 10. That factor will make the result be a multiple of 11. Since the LCM is 2520, and that has a remainder of 1 modulo 11, we know we must multiply it by 10 before adding 1 in order to get a multiple of 11.

That is, the lady has 2520×10 +1 = 25201 eggs.

2x^2+5x+17

your welcome. : )

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1