Question

Sandwich A costs 4$, sandwich B costs 0.5$ and sandwich C costs 0.25$. In total, 20 sandwiches are sold and the total cost was 20$. How many of each sandwich were sold?

Answer 1

A+B+C=20 (total sandwiches sold)
4A+.5B+.25C=20 (total cost of sandwiches)

are the two equations that must be true. Multiplying the 1st equation by 4 gives us 4A+4B+4C=80. If we subtract the 2nd equation from 4A+4B+4C=80 we get 3.5B+3.75C=60. This equation has infinitely many values of B and C that satisfy it, however B and C must be non-negative integers. Since the number of sandwiches sold is 20, then the value of B and C must be one of 0, 1, 2, ..., 20. By trial and error, we get B=15, C=2. This then means A=3.