Sunday, May 17, 2009

Algebra Challenge

Weight Watchers uses a formula that takes into account total calories, grams of fat, and grams of fiber to assign point values to foods. According to the Weight Watchers formula, a McDonald's hamburger is worth 5 points, a McDonald's cheeseburger is worth 7 points, and a McDonald's double cheeseburger is worth 10 points. According to McDonald's, the hamburger has 250 calories, 9 grams of fat and 2 grams of fiber; the cheeseburger has 300 calories, 12 grams of fat, and 2 grams of fiber; and the double cheeseburger has 440 calories, 23 grams of fat, and 2 grams of fiber.

What is the Weight Watchers formula?

The photo above, of the McDonald's double cheeseburger, comes from


Ed McMahon said...

Divide the Weight Watchers membership fee by your available credit.

If your credit = > 100% of the membership fee, join up and we'll give you the answer.

P.S. You may already be a loser.

DaveinHackensack said...

I guess algebra wasn't a prerequisite for dental school in the 1970s.

JK said...

The formula is

(Cal + (Fat x 4) - (Fiber x 10))/

All of the point values assigned were rounded.

I admit, after a few minutes of mental labor, I turned to Google. (Sad, sad state of affairs.)

I'm curious to know how you figured out the formula given the information provided, when the value of grams fiber was a constant and thus you had no way to directly assess Fiber's variability within the function, just of Calories and Grams Fat.

Perhaps I'm way rusty here, and there's an algebra formula I've forgotten in the years I've spent out of school. So school me, Dave.

DaveinHackensack said...

In hindsight, using three items with the same grams of fiber might have made this seem more confusing than necessary. I just picked the first three items on the McDonald's nutritional chart. But I don't think it should have made a difference -- and in fact, should have made it a little easier to solve.

Of course, you can't solve one equation with three unknown variables, but using algebra you can solve a system of three equations, each of which contain the same three unknown variables. With the three burgers, you can construct three equations, and manipulate them to cancel out variables. Having the same constant (2) assigned to the fiber variable should make that a little easier.

I doubt you'd see this example used on a test such as the GMAT though, since the size of the calorie numbers in relation to the others would make the arithmetic time consuming without a calculator.

JK said...

Yes, you know what, I was probably making it more complicated than I had to because I was try to bang it out on a sheet of scrap paper here at my desk, so I needed a short way to do it. No TI-89 here. In fact I think I need to buy another one, having misplaced mine a long time ago. (Fun toys to program, they are. I used to play/make games on it in calculus class to pass time.)

300x + 12y + 2z = 7
250x + 9y + 2z = 5
440x + 23y + 2z = 10

Without going through the drudgery of solving it on paper to check, I don't think the equation derived from from the data provided would match the weight watchers formula too well because the points were so crudely rounded, so the formula one derives from the data in this post is probably much more messy than the clean one I pulled off google. For example, 7.44 in the Weight Watchers equation became just "7", etc.

Jimmy Kimmel said...

Goldman Saks put out a blanket recommendation on all the
'diet plan' stocks today...

Their advice...

OVERWEIGHT the group.

DaveinHackensack said...

That's a good point about the rounding Weight Watchers uses in its formula, J.K. Another reason this would have been a bad standardized test problem.