### 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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