It would be too cold to go anywhere even if there were anywhere to go, the bathrooms are clean, and I'm feeling the force of the maxim concerning how all the ills of the world may be traced to the inability of people to be alone with their thoughts. I'm on a medication, a blood thinner, that is not supposed to be used with alcohol, so probably it's lucky that my 7th-grader has a math problem she can't get:

Oliver, Ros, and Alice want to start a petting zoo. They decide the best animals to have are hippos, monkeys, and zebras. Oliver decides to buy 7 hippos, 10 monkeys, and 3 zebras for a total of $151. Ros decides to buy 5 hippos, 2 monkeys, and 9 zebras for a total of $185. Alice buys 4 hippos, 6 monkeys, and 5 zebras for a total of $137. What is the cost for each animal? Set up and solve this system of equations using any method of your choice. Show your work!

Actually, this was a question on a test, and Lydia showed it to me as an example of how outrageously unreasonable her teacher is. As she explains it, you get graded on a 4-point scale, and for a 4 you have to get the "bonus problem" right. The above was the bonus problem. How can anyone except "Mickey, the class genius," possibly get a 4 when "Ms. Novak's never showed us what to do if there are three variables!" Etc., etc., Ms. Novak is a tyrant, etc. I say maybe Ms. Novak wants to see who can apply what they know to a new kind of problem and who will just throw their hands in the air and moan. Now I'm in the same moral category as Ms. Novak, but hell if I'm going to agree that the teacher's expectations are too high. Put on your thinking cap, Whiney McWhinerson!

She'd actually made a good start—the "setting up the system of equations" part:

7h + 10m + 3z = 151

5h + 2m + 9z = 185

4h + 6m + 5z = 137

It was at this point that she'd thrown her arms in the air, or maybe just hoped for partial credit on the dreaded bonus problem. She can solve the problems with two equations and two variables, and the method is pretty much the same: you "manipulate" the equations to eliminate variables and make apt "substitutions." The permitted "manipulations" are multiplying any of the equations by the same constant, and adding (or subtracting) one equation from another (which amounts to adding the same quantity to both sides of an equation). The more variables, the more "manipulations," but it can be fun if it's cold out and you're a big nerd.

Like, with these equations, it might be useful to subtract the third one from the second, because then you will get an expression for h that can be substituted into other equations:

5h + 2m + 9z = 185

4h + 6m + 5z = 137

h – 4m + 4z = 48-------->h = 48 + 4m – 4z

Now, in the first original equation, substitute "new h" for "plain old h":

7(48 + 4m – 4z) + 10m + 3z = 151

336 + 28m – 28z + 10m + 3z = 151

38m – 25z = –185**25z - 38m = 185**

We can then substitute "new h" for "plain old h" in, say, the third original equation:

4(48 + 4m - 4z) + 6m + 5z = 137

192 + 16m - 16z + 6m + 5z = 137

22m - 11z = -55

2m - z = -5

z = 2m + 5

That worked out nice!—an expression for z that can be substituted into the equation highlighted above:

25(2m + 5) - 38m = 185

50m + 125 - 38m = 185

12m = 60

m = 5

If m is 5, z is 15 (since z = 2m + 5—we're "back substituting" now). And if m is 5 and z is 15, we can substitute those values into one of the original equations to find that h is 8. To be OCD (obsessive compulsive disorder) about it, substitute all 3 values into the original 3 equations to make sure it checks out, and it does. Hippos are $8, monkeys are $5, and $15 for a zebra.

Only two hours now till the Gopher basketball game, and some of that time will be taken up by making supper, and eating it, and cleaning up afterwards. Pump out those vaccines, man—though I won't need one if we lose to Nebraska.

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