SOLUTION: A bag contains 42 coins, with a total weight of 246 grams. If the bag contains only gold coins that weigh 8 grams each and silver coins that weigh 5 grams each, how many gold and h
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Question 4012: A bag contains 42 coins, with a total weight of 246 grams. If the bag contains only gold coins that weigh 8 grams each and silver coins that weigh 5 grams each, how many gold and how many silver coins are in the bag? Answer by Earlsdon(6294) (Show Source):
You can put this solution on YOUR website! Let G = number of gold coins and S = number of silver coins.
(1) G + S = 42 Total number of coins in the bag.
(2) G(8 gms) + S(5 gms) = 246 gms. Total weight of coins.
Rewrite (1) as G = 42 - S and substitute this for G in (2).
(2a) (42 - S)(8 gms) + S(5gms) = 246 gms. Solve for S.
336 - 8S + 5S = 246
336 - 3S = 246 Subtract 336 from both sides.
-3S = -90 Divide both sides by -3
S = 30 The number of silver coins.
G = 42 - S
G = 42 - 30
G = 12 The number of gold coins.
Check: G + S = 12 + 30 = 42 The total number of coins.
G(8 gms) + S(5 gms) = 246 gms
12(8) + 30(5) = 96 + 150 = 246 gms. The total weight of the coins.
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