MathBench > Miscellaneous

Tricks with Division

The 3 Little Pigs go on a diet

One year not too long ago, the three little pigs decided they needed to lose weight. The first little pig, sitting on his porch made of straw, declared that he didn't need a diet to lose weight, he would just start eating less. The second little pig, leaning against his stick windowframe, announced he had found a great grapefruit diet in Good Stykeeping magazine. The third pig started a Weight Watchers group in his comfortable brick living room.

three pigs

In the first month (December), the first little pig ate a gingerbread house ("calories don't count if eaten secretly"), 3 fruit cakes ("if it doesn't taste good, it doesn't have calories"), and a vat of creamed spinach dip ("spinach automatically destroys all calories of the food it is added to"). The second little pig consumed 147 grapefruits, while the third little pig discussed quiche makeovers.

In the second month, the first little pig gave up ("the calories are obviously not following the rules"), the second little pig discovered that the local supermarket does not stock grapefruits in January and switched to popcorn balls instead, and the third little pig discovered nonfat sour cream.

The table below shows the weight of each little pig over the two months of their weight loss efforts:

  Dec 1 Dec 15 Jan 1 Jan 15 Feb 1
Little Pig #1 190 192 194 199 204
Little Pig #2 170 164 158 156 154
Little Pig #3 295 290 285 280 275
'

What was the rate of weight change at beginning of the diet say, the first two weeks)?

What are my units?

Subtraction
Ratio / Fraction
proportion
percent
percent change

 

What proportion of total change occurred in first month?

What are my units?

Subtraction
Ratio / Fraction
proportion
percent
percent change

 

big pigAfter 2 months, the pigs get together. While Pig 1 drowns his sorrow in a 7-layer salad, pigs 2 and 3 get into an increasingly loud argument about who lost more weight. Pig 3 claims that simple arithmetic proves he's the winner, while pig 2 complains that this is hardly fair, given that pig 3 had so much more to lose in the first place...

How would you determine which pig lost the most weight?

What are my units?

Subtraction
Ratio / Fraction
proportion
percent
percent change

 

Notice that the all-important question "who wins" depends on what you care about. If you want to "handicap" the results by taking the starting conditions into account, then you should use percent change. Proportion and percent will give you the same information, but in a way that is harder to interpret.

If, on the other hand, all you care about is the cold, hard number of pounds down on the scale, then you should avoid percent change and just use subtraction. Subtraction will NOT give you the same information as using percent change (or percent or proportion), so only use it when the initial conditions do not matter!

 

 

 

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