I was at a restaurant the other day, and there was a sign that said,

"Each of our omelets is made with three eggs."

When I looked at the menu, the first three omelets were:
      Cheese omelet: 7-dollars-45-cents.
      Bacon omelet: 7-dollars-70-cents.
      Bacon and cheese omelet: 8-dollars-45-cents.

What does a plain omelet cost? (Just eggs, no bacon, no cheese).

Solution to the Problem:

The answer is $6.70 for an egg omelet.

If the cheese omelet is $7.45, and the bacon and cheese omelet is $8.45, then the bacon must cost a dollar.
So if the bacon omelet is $7.70 and we know that the bacon costs a dollar, then subtract $1 and you get $6.70 for an egg omelet.

Brijesh Dave sent in two different ways to solve the problem:

Let the cost of plain omelet be E cents.
Cost of cheese in omelet be C cents.
Cost of Bacon in omelet be B cents.

Now sign on restaurant says
"Each of our omelets is made with three eggs."
Which means each of omelet is mixture of plain omelet and either Cheese or Bacon or both ingrediants.

Now according to condition of problem

E + C = 745.............(1)
E + B = 770.............(2)
E + B +C =845.........(3)

Adding eqn.(1) & (2)
2E + B + C =1515.........(4)

Subtracting eqn (3) from (4)

E = 670
B = 100
C = 75

Therefore cost of plain omelet is $ 6.7
Cost of Cheese in plain omelet is $1
Cost of Bacon in omelet is $0.75

Alternative solution
Cheese omelet + Bacon Omelet = $ 15 .15 ... (A)
Cheese and Bacon omelet = $ 8.45................(B)

Plain omelet = $6.7 ........(A) - (B)

Correctly solved by:

1. Jim Hooker Johnson City, Tennessee
2. James Alarie Flint, Michigan
3. Jonathan Punke Waukegan High School,
Waukegan, Illinois
4. Marivi Bungay-Domingo Philippines
5. Braydon Saxton Mountain View High School,
Mountain View, Wyoming
6. Alyx Wells Mountain View High School,
Mountain View, Wyoming
7. Cailee Hamilton Mountain View High School,
Mountain View, Wyoming
8. Brijesh Dave Mumbai city, Maharashtra, India
9. Wyatt Gross Mountain View High School,
Mountain View, Wyoming