Math! : A Quick Peek Inside My Brain

Dear every school child ever who said, "Why am I learning this math? I'll never use it in real life."

False. You will use all kinds of math on a daily basis. Calculating tax on your purchases (unless you're European, whose prices are all-inclusive), determining how much tip to leave (unless you're European, who don't tip), remembering all the ratios and conversions of weight and length measurements (unless you're European, who use the easily remembered Metric system, wherein you just move the decimal place). See? All the time!...(unless you're European.)

Essentially, all my supplies

Regardless, I thought I was going to have to use some math skills to prepare my dinner the other night. As I may or may not have mentioned, the only utensils and cooking implements that came with my apartment were: one (1) frying pan, one (1) pot, two (2) plates, two (2) bowls, two (2) small glasses, one (1) coffee cup, two (2) knives, two (2) forks, three (3) spoons and one (1) spatula. Note the absence of a measuring cup.

So, I was attempting to make some "just add boiling water to this powder" soup. The instructions called for 175mL (milliliters) of water to be added to the powder. Again, I did not have a measuring cup. However, what I did have were some empty bottles, including some 25cL (centiliters) Panach' bottles and a 50cL Evian bottle. And I was quickly recalled to those classic math teasers, similar to the one you may have seen in Die Hard with a Vengeance - the water jug problem.

And here is my legitimate, actual thought process:

"I can do this," I tell myself. "Ok, first of all, 1 cL = 10 mL, easy enough. So what I have are a 250mL (25cL) and a 500mL (50mL) bottle. Also, I have my coffee cup which is...*fills up 250mL bottle, pours into cup, goes right to the top*...also exactly 250mL. Hrm, so I need 175mL. Half of 250 is 125. These drink bottles are oddly shaped, but I could precisely gauge "half" of this perfectly cylindrical 250mL coffee mug to reach that 125mL. [I could tear a strip of paper the same length as the height of the cup, then fold it in half to find the exact center point; ie, half of the cup, thus 125mL.] So, if I can get 125mL of the 175mL I need, that just leaves 50mL more. That's 1/5 of the 250mL or 1/10 of the 500mL. That's slightly more challenging, and, unfortunately these containers are in multiples of each other (250*2=500), so it's not as easy as the 3gallon and 5gallon to get 4gallons in Die Hard with a Vengeance. Although, I do have this coffee cup which I can use to find 125mL. So, if I have my 500mL full, and pour into the coffee cup until it's half full, that would be 500-125=375mL left in the 500mL container. Well, unfortunately there seems to be no way to get exactly 50mL. I guess I could fill the 250mL coffee cup and then proportion it out equally between five of the Panach' bottles, making sure the water levels all line up. And that's 250/5=50mL that I need..."

A luxury

By this time, the water had started boiling. And that's when I realized that I was measuring water for soup, not measuring rocket fuel for a spaceflight. And that I get waaay too caught up in solving a problem when it's not that important. So what I ended up doing was just eyeballing half of coffee cup (125mL) and then eyeballed 1/5 to 1/4 (right around the 50mL I needed). After all...soup, not rocket fuel.

Ok, so I didn't actually do that much math. But I *almost* did. So, stay in school, kids. Or...move to Europe. Whatever.


Also, if someone had told me how nasty the "soup" was going to be, I wouldn't have wasted my time thinking about it. I wouldn't even have wasted boiling the water to make it. I ate about three spoonfuls and then threw out the rest. (And then I tried to calculate how much water was in those three spoonfuls....kidding.)

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I'm sorry if you came here for actual math and were sorely disappointed. I won't leave you that way. I'll leave you with an actual math problem that I ironically came across in the book I was reading - Simple Genius by David Baldacci - on the same day as my kitchen mathematics:

"Suppose I'm a grandfather, and I have a grandson who is about as many days old as my son is weeks old. And my grandson is as many months old as I am in years. Together, we all are 140 years old. How old am I (the grandfather) in years?"

Have fun! and STOP HERE if you want to do the problem on your own. Otherwise, read below to follow the method I took. At the very bottom is the answer.

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Here's my approach:

Variables:
O=grandfather (old), S=son, Y=grandson (young)
d=age in days, w=age in weeks, m=age in months, y=age in years

Assumptions (facts):
7 days = 1 week
52 weeks = 1 year
12 months = 1 year

The Problem / Givens (in equation format):
Yd = Sw ... (Grandson is as many days old as son is weeks old)
Ym = Oy ... (Grandson is as many months old as grandfather is years old)
Yy + Sy + Oy = 140 ... (All three ages together are 140 years old)

The Solution:
Ym = 12Yy   [fact]
Ym = Oy   [given]
thus
12Yy = Oy   [1]

Yy + Sy + Oy = 140   [given]
using [1] substitution
Yy + Sy + 12Yy = 140   [2]

Sw = 52Sy   [fact]
Yd = Sw   [given]
thus
Yd = 52Sy
Sy = Yd/52   [3]

Yd = Yy*52*7   [fact, days = years * 52weeks/year *7 days/week]
Yd = 364Yy   [4]

Combining [3] and [4]
Sy = Yd/52 = (364Yy)/52 = 7Yy
Sy = 7Yy   [5]

Yy + Sy + 12Yy = 140   [from [2]]
substitute [5]
Yy + 7Yy + 12Yy = 140
20Yy = 140
Yy = 7   [6]

12Yy = Oy   [from [1]]
substitute [6]
12*7 = Oy
Oy = 84   [7]

Yy + Sy + Oy = 140   [given]
sub [6] and [7]
7 + Sy + 84 = 140
Sy = 49   [8]

So there you are. The grandfather is 84 years old. The son is 49 years, and the grandson 7 years.