(Image: Lucasfilm)

Bob Swanek's son Cody was asked to take an algebraic expression and build a word problem from it. The result of his efforts is a gloriously rich tale about the composition of the next Star Wars film. J.J. Abrams, the director of that movie, is facing some serious problems:

J. J. Abrams is making Star Wars Episode 7. He rented three speeder bikes which was 700 imperial credits to start. He must pay 100 imperial credits to keep his speeder bikes daily. If he does not pay daily, Prince Xizor and other Black Sun members will kidnap J. J. Abrams, bring him to Mustafar, and sacrifice him.

J. J. Abrams is also paying 5 bounty hunters to keep separatist spies out. That costs 200 imperial credits to start, then 50 imperial credits for each bounty hunter every time they capture a spy. The Separatists send 2 spies every day.

In how many days does J. J. Abrams spend the same amount of imperial credits on speeders and bounty hunters?

(Photo: Bob Swanek)

-via 22 Words

The assumption of the question would not be the bounty hunters are paid 200 + 50 per spy a day but the Bounty Hunters receive 200 credits up front then 50 credits a spy. Since they each get 50 credits per spy captured, with 5 bounty hunters, that would be 50 * 5=250 a spy. With 2 spies a day that makes 500 credits a day. So, assuming no spies are sent the first day the bounty hunters are hired then the equation should be 200 + 500(t-1)= 700 + 100(t-1). Or if there are bounty hunters are sent the first day than 700+500(t-1)=700+100(t-1). I would assume the first equation would be what the student is looking for based on the last part of the question.
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The correct answer, of course, is "Stick to Star Trek, J.J."
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You're right. Looks like I failed the test! Good thing it's too late to take away my math degree. :)
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I believe your equation is incorrect, since it shows 500 and not 700 as the initial cost of the speeders.

It's also possible that the bounty hunters get paid a base rate of 200 per day and 50 per spy, and that the spies are available on the first day. We'd also have to assume that we don't have to pay the daily rent for the first day for the speeders.

Using my interpretation, the formula would be 300t = 700 + 100(t - 1), in which case t = 3. (Edited for an error of my own.)
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Yes, some information is missing. If we use the assumption that there is a definite answer then it's possible to resolve the ambiguities. The problem doesn't specify the capture rate. The only reasonable guess is that the bounty hunters capture 2 spies per day. (Otherwise they might capture only 1 during the first year, then 600 on a single day.) If the capture of a spy results in 50 credits to a single bounty hunter, then the maximum average daily payout is 100 credits. This equals the speeder bike rental, which means there is no solution. Instead, the only reasonable guess is that each bounty hunter gets 50 credits, giving a payout of 250 credits per day. The cost equation is 200 + 250*t = 500 + 100*t which has an answer of exactly t=2 days. Problems for this grade level love to have integer solutions, which helps support the conclusion that this is the expected answer.
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