1) p = b + 4v

2) m = (p - 4) + 2c + 3v

3) m - p = b

4) b + c = 11

There are four equations with 5 unknowns - no direct solution possible.

Therefore, we create four equations, where the four icecreams are dependent on only the fifth:

1) Clean up 4th equation

b + c = 11 =>

b = 11 - c

2) Replace b in 1st, 2nd, and 3rd equation

p = 11 - c + 4v

m = p - 4 + 2c + 3v

m - p = 11 - c

3) Combine 2nd and 3rd equation

m = p - 4 + 2c + 3v

m - p = 11 - c => m = 11 - c + p

p - 4 + 2c + 3v = 11 - c + p =>

-4 + 2c + 3v = 11 - c =>

2c + 3v = 15 - c =>

3v = 15 - 3c =>

v = 5 - c

4) Replace b and v in first equation

p = 11 - c + 4(5 - c) => p = 11 - c + 20 - 4c =>

p = 31 - 5c

5) replace p and b in 3rd equation

m - (31 - 5c) = 11 - c => m - 31 + 5c = 11 - c => m = 11 - c + 31 - 5c =>

m = 42 - 6c

5) We now have four equations:

b = 11 - c

v = 5 - c

p = 31 - 5c

m = 42 - 6c

In the 2nd quation we can see, that c spans from 1 to 4, so these values will be inserted in the equations:

c = 1; b = 10, v = 4, p = 26, m = 36

c = 2; b = 9, v = 3, p = 21, m = 30

c = 3; b = 8, v = 2, p = 16, m = 24

c = 4; b = 7, v = 1, p = 11, m = 18

There is only one correct solution, where one of the ice creams wil cost 16 gold; the one where c costs 3 gold.

You bought the pink one.

This was fun, thanks:-)

Kyhl, COM201 Big Ben