SOLUTION: The Swanzy arcade in Accra uses 3 different colored tokens for their game machines. For $20, you can purchase any of the following mixtures of token. 14 gold, 20 silver and 24 bron

Question 1099450: The Swanzy arcade in Accra uses 3 different colored tokens for their game machines. For $20, you can purchase any of the following mixtures of token. 14 gold, 20 silver and 24 bronze: OR, 20 gold, 15 silver and 19 bronze: OR, 30 gold, 5 silver and 13 bronze. What is the monetary value of each token?
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Let g, s, and b represent the numbers of gold, silver, and bronze tokens.

(1)
(2)
(3)

To solve the system by hand, I see that the coefficients of s in the three equations are multiples of 5, so I would use elimination to reduce the system to two equations in g and b.

3 times equation (3) minus equation (2) gives or (4)
4 times equation (3) minus equation (1) gives or (5)

5 times equation (5) minus 7 times equation (4) eliminates b, giving us , so g = 0.5

Substituting back in earlier equations then gives us s = 0.35 and b = 0.25.
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