Round 20

Date released: August 2nd, 2001.
Date rewarded: August 10th, 2001.

The economy of Roo Island is rather strange. They have four coins, each worth a different number of Neopoints. Three red coins plus two Neopoints equal a green coin. Three green coins plus five Neopoints equal a purple coin. Eleven red coins plus a single Neopoint equal a purple coin.

The fourth coin is a silver coin that is worth four purple coins. If I go to the Roo Island bakery and buy a loaf of bread worth 84 Neopoints with my silver coin, and the shopkeeper gives me change in red coins... how many red coins would I get?

Prize
Unknown

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Let r, g, p, s be the values of red, green, purple and silver coins respectively. We know that:

* Three red coins plus two Neopoints equal a green coin:

3r + 2 = g (1)

* Three green coins plus five Neopoints equal a purple coin:

3g + 5 = p (2)

* Eleven red coins plus a single Neopoint equal a purple coin:

11r + 1 = p (3)

* Silver coin is worth four purple coins:

s = 4p (4)

From (2) and (3), we have:

3g + 5 = 11r + 1 <=> 11r = 3g + 4 (5)

From (1) and (5), we have:

11r = 3g + 4 = 3 * (3r + 2) + 4 = 9r + 10 <=> 2r = 10 <=> r = 5

Therefore:

g = 3r + 2 = 17
p = 3g + 5 = 56
s = 4p = 224

The change that I should get (in red coins):

change = (224 - 84) / 5 = 140 / 5 = 28

I should get back 28 red coins.