Housewife Algebra

My teenage son came home with a difficult algebra problem.  He is pretty smart in math, but didn't know the "formula" for this one:  Jane bought some styrofoam cups.  One package of 12 -  6 oz. cups cost blah.  Another package of 12 - 4 oz. cups cost blah-blah.    She purchased 10 packages of cups.  She spent a total of blabbity-blah.  How many of each package did she buy?

I put on my reading glasses.  I read the problem.  My son stood by rolling his eyes. 

"Well,"  I said.  "I know how to figure this out the "housewife" way, but I couldn't show my work on paper."

"Mom, just forget it.  I will ask the teacher at lunch tomorrow."

"Wait!" I pleaded, trying to remember what I learned in algebra over 30 years ago.  Then I did some quick estimating, rounding-up, and adding in my head.  "I would say that Jane bought 4 packages of  6 oz. cups and 6 packages of 4 oz. cups.

Then I checked my math.  Bingo, Baby.  Correct answer.

"Mom, that's called "guess and check" and my teacher won't accept it," he said, trying to let me down gently.  "I have to show my work."

He collected his math book and headed upstairs before I could lecture him on some "real life" algebra.

For example, if I am inviting 20 friends to my house for a party, how many bottles of wine do I purchase if the average person consumes 4 oz. of wine per half hour?  First, my friends drink way more than the average 8 ounces of wine per hour.  (See how I quickly figured out the hourly consumption in my head?)  Second, I would just buy 8 bottles plus some beer and vodka.  Besides, everyone knows that my friends would come to the party with a bottle of wine for the hostess.

Next example would be if I were going on a car trip and wanted to calculate my gas mileage.  Simple.  I would just push the gas mileage button on my dashboard and it would be displayed.

Rocket scientists are the only ones I can think of that would have to calculate the exact amount of rocket fuel used to go to the moon using algebra.  And show their work.

But even then, wouldn't they top off the fuel tank?

Just in case.

-Lela
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