Brain Teasers
Video Visions
Tobin is thinking of joining a video club. He received this offer in the mail:
"Buy 7 videos for just 1 penny apiece! (You must follow either Plan A or Plan B.)
Plan A: Buy 2 more videos for $6.95 each with your initial order. Then buy only 3 more videos over the next 3 years at regular club prices.
Plan B: Buy only the 7 videos for 1 penny apiece. Then buy 5 videos over the next 3 years at regular club prices.
Regular club prices: Each video normally costs between $19.95 and $39.95.
Send no money now. We'll bill you later."
Tobin has $23.00 in an empty peanut-butter jar in his room, so he estimates he can afford to send for the 9 movies because they will cost around $14.00. Tobin tells his Uncle Ben about the video deal, and his uncle says, "Tobe, do yourself a favor and look through the fine print to find out how much they're actually going to bill you for those videos." Tobin finds this information:
Shipping and Handling
For the first 7 movies ... $1.60 each
For additional movies ... $1.70 each
State sales tax on all purchases is 3%.
How many videos can Tobin afford to order right now? Then, how much would it cost Tobin for his total of 12 videos over the next 3 years, using an average of the regular club prices?
"Buy 7 videos for just 1 penny apiece! (You must follow either Plan A or Plan B.)
Plan A: Buy 2 more videos for $6.95 each with your initial order. Then buy only 3 more videos over the next 3 years at regular club prices.
Plan B: Buy only the 7 videos for 1 penny apiece. Then buy 5 videos over the next 3 years at regular club prices.
Regular club prices: Each video normally costs between $19.95 and $39.95.
Send no money now. We'll bill you later."
Tobin has $23.00 in an empty peanut-butter jar in his room, so he estimates he can afford to send for the 9 movies because they will cost around $14.00. Tobin tells his Uncle Ben about the video deal, and his uncle says, "Tobe, do yourself a favor and look through the fine print to find out how much they're actually going to bill you for those videos." Tobin finds this information:
Shipping and Handling
For the first 7 movies ... $1.60 each
For additional movies ... $1.70 each
State sales tax on all purchases is 3%.
How many videos can Tobin afford to order right now? Then, how much would it cost Tobin for his total of 12 videos over the next 3 years, using an average of the regular club prices?
Hint
1. Break down the problem into smaller problems.2. Shipping and handling charges should not be taxed.
Answer
Tobin can afford to order only 7 videos right now. The total cost for all 12 videos will be $174.01.Plan A: Tobin will pay $ .07 + (2 * $6.95) = $13.97 for the first 9 videos. With a 3% sales tax, the videos will cost $14.39. However, Tobin must also pay for the shipping costs: (7 * $1.60) + (2 * $1.70) = $14.60, boosting the total price of the first 9 videos to $28.99. He cannot afford this right now, so he must consider Plan B.
Plan B: Tobin's initial order will cost $ .07 (including sales tax) + (7 * $1.60) for shipping and handling = $11.27. The average club price is ($19.95 + $39.95) / 2 = $29.95. So the remaining 5 videos will cost 5 * $29.95 = $149.75. With a 3% sales tax, the videos will cost $154.24 + (5 * $1.70) for shipping and handling = $162.74. Adding the cost of the first 7 videos to the cost of the other 5 gives a total cost of $174.01.
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