## Tuesday, December 13, 2011

### this week's Math Beast Challenge problem

From here:

"Walter's Exercise"

Every day, Walter burns 500 calories from cardio exercise. On some days, he also burns an additional 600 calories from weight training. If, over a 240-day period, Walter burns an average of 850 calories per day from cardio exercise and weight training combined, then on how many more days did Walter engage in both cardio exercise and weight training than in cardio exercise only?

(A) 40
(B) 60
(C) 80
(D) 100
(E) 140

My answer will appear in the comments, but if you figure this out before I write anything, don't hesitate to leave your comment.

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1. The answer is (A) 40.

Let x = days of cardio alone @ 500 cal/day and let y = days of cardio and weight training @ 1100 cal/day.

We can set up simultaneous equations as follows:

(1) x + y = 240

(2) 500x + 1100y = 240(850) = 204000

Simplifying (2), we get 5x = 2040 - 11y
From (1) we know that x = 240 - y, so 5x = 1200 - 5y

1200 - 5y = 2040 - 11y

6y = 2040 - 1200 = 840

y = 840/6 = 140

From (1), we know that x = 100

The answer to the question is y - x, which equals 40.

2. I hit "publish" on your comment but refused to look at the answer so that I could try solving this for myself. It's scary that we ended up using exactly the same method. I agree that the answer is (A).

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