The cheerleading team is selling gift baskets as a fundraiser. Each basket will contain 3 different sizes of candles: small, medium, large. Small candles cost $1 each, medium $4 each, and large candles cost $6 each. The team has decided to sell baskets containing 8 candles for $24 each. Each basket contains as many small candles as medium and large combined. How many small candles are in a basket?
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This may seem long, but bear with me for a while: Let a = the number of small candles b = the number of medium candles c = the number of large candles From: "The team has decided to sell baskets containing 8 candles", we get: a + b + c = 8 a = 8 - b - c Call this equation 1 From the prices, we get: a + 4b + 6c = 24 Call this equation 2 From the last statement, we get: a = b + c Call this equation 3 ------------------------------------- Equating 1 and 3, we get b + c = 8 - b - c 2b = 8 - 2c b = 4 - c Call this equation 5 Substituting 1 in 2, we get: (8 - b - c) + 4b + 6c = 24 8 + 3b + 5c = 24 3b + 5c = 16 Call this equation 6 Substituting 5 in 6, we get 3(4 - c) + 5c = 16 12 - 3c + 5c = 16 2c = 4 c = 2 Substituting the value of c in 5, we get: b = 4 - 2 b = 2 Substituting the values of b and c in 1, we get a = 8 - 2 - 2 a = 4 They sell 4 small, 2 medium and 2 large candles in every basket.
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