A tennis club is organizing group lessons. The club supplies each player with 40 new balls, which costs the club $1 each ball. Each player pays $300 for the lessons. The club must pay each instructor $1,000 for conducting the lessons, and there must be at least 1 instructor for every 6 players. Which amount of players and instructors meets these requirements and still gives the club a net profit? Choose 1 answer: A 6 players and 2 instructors (B) 10 players and 3 instructors (C) 13 players and 2 instructors (D) 16 players and 3 instructors

Question

A tennis club is organizing group lessons. The club supplies each player with 40 new balls, which costs the club  $1 each ball. Each player pays  $300 for the lessons. The club must pay each instructor  $1,000 for conducting the lessons, and there must be at least 1 instructor for every 6 players. Which amount of players and instructors meets these requirements and still gives the club a net profit? Choose 1 answer: A 6 players and 2 instructors (B) 10 players and 3 instructors (C) 13 players and 2 instructors (D) 16 players and 3 instructors

Bytelearn · Accepted Answer

Calculate net income per player: Let's first calculate the net income per player. Each player pays $300 for the lessons.Calculate cost per player for the club: Now, let's calculate the cost per player for the club. The club supplies each player with 40 balls, and each ball costs $1. So, the cost for balls per player is 40 balls * $1/ball = $40.Calculate net income from each player: Subtract the cost of balls from the payment each player makes to find the net income from each player. $300 (payment) - $40 (cost of balls) = $260 net income per player.Calculate cost of instructors: Next, we need to calculate the cost of instructors. There must be at least 1 instructor for every 6 players, and each instructor costs the club $1,000.Analyze answer choice (A): Let's analyze each answer choice to see which one gives the club a net profit:  (A) For 6 players and 2 instructors: Net income from players = 6 players * $260/player = $1560. Cost for instructors = 2 instructors * $1,000/instructor = $2,000. Net profit = $1560 - $2,000 = -$440 (a loss, not a profit).Analyze answer choice (B): (B) For 10 players and 3 instructors: Net income from players = 10 players * $260/player = $2,600. Cost for instructors = 3 instructors * $1,000/instructor = $3,000. Net profit = $2,600 - $3,000 = -$400 (a loss, not a profit).Analyze answer choice (C): (C) For 13 players and 2 instructors: Net income from players = 13 players * $260/player = $3,380. Cost for instructors = 2 instructors * $1,000/instructor = $2,000. Net profit = $3,380 - $2,000 = $1,380 (a profit).Analyze answer choice (D): (D) For 16 players and 3 instructors: Net income from players = 16 players * $260/player = $4,160. Cost for instructors = 3 instructors * $1,000/instructor = $3,000. Net profit = $4,160 - $3,000 = $1,160 (a profit).Check instructor-to-player ratio for (C): Now we need to check if the number of players to instructors ratio is met for the profitable options:  (C) 13 players with 2 instructors is more than the required ratio of 1 instructor per 6 players. (D) 16 players with 3 instructors is also more than the required ratio of 1 instructor per 6 players.Check instructor-to-player ratio for (D): Since both (C) and (D) are profitable and meet the instructor-to-player ratio, we need to choose the one that gives the highest profit. Comparing the net profits, option (C) gives a higher profit than option (D).

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