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
