## Can someone help me improve this problem? (U-Haul rental rates ; systems of linear functions)

So the Emergent Math family moved houses this weekend (editor’s note: they didn’t actually move the houses, they moved the furniture inside the houses). We were given basically three different options for U-Haul rentals of increasing size and increasing price. This led me to believe that a nice systems problem could be constructed from this.

I still feel that way, but it sort of got away from me. I think the idea of deciding whichtruck to rent + various mileage costs is pretty decent. But then things sort of spiraled out of my control and I ended up with a convoluted problem that was actually kind of tedious.

So I’m asking my faithful readership to help me out. I’ve split the problem up into two pieces – as I probably would have in a classroom setting. Help me make this problem better!

Basic gist of the problem:

Moving houses (ed. note: again, just the furniture – the author was not living in a double-wide). Three different U-Haul options of increasing square footage (733, 865, and 1015 cubic feet) with three different up-front costs for the U-Haul (\$19.95, \$29.95, and \$39.95, respectively). Also, mileage costs \$0.79 per mile – hence thenice linear functionality of the problem. Determine which U-Haul I should rent.

Documents (Part 1 and 2) below.

Best improvement to the problem gets a free oven mitt!

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### 2 Responses to Can someone help me improve this problem? (U-Haul rental rates ; systems of linear functions)

1. Wes says:

This problem has a lot of messiness, which is good for PBL. However it is more a min/max problem, because you don’t really know how many trips each of these trucks will need. I.e., the biggest truck could be anywhere from 2 to 5 trips. Perhaps plotting the points would result in a general area of costs on a grid.