Solving Calories Problem: Lose 6kg in 42 Days

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Homework Statement



By taking 'daily input' of 2200 kcal your body weight doesn't change. If you decide to lower your 'daily input' for 700 kcal, you will lose 100 grams a day. You want to lose 6 kg in the next 42 days. How big is your 'daily input' going to be?

The Attempt at a Solution



Basically, I've solved this in two ways, and both give different solutions.

6000 grams are in 6 kilograms, so 6000 over 42 days I will keep as 6000/42.

1) 700 kcal : 100 g = x : 6000/42
x = 7*6000/42 = 42000/42 = 1000 kcal. Therefore the 'daily input' will be 1200 kcal (2200-1000).

2) 2200-700=1500 kcal.

x : 1500 kcal = 100 : 6000/42
x = 1500 * 100 * 42/6000
x = 1050 kcal. Therefore our 'daily input' will be 1050 kcal.

Obviously these answers don't match, so which answer is correct?
 

Discussion

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The implicit assumption is that the weight loss (or gain) is proportion to the deficit (or surplus) of calories input. So you want to work with relative amount, the 700kcal.
 
Hmm.. First we must find the correct equation.

One way to approach this is:

If you remove 700 kcal from your diet, you lose 100 grams.. If you remove 700*60kcal totally over n number of days (with n being sufficiently large), you lose 6kg.. That is 42000 kcal. Our n is equal to 42. Thus, you must divide 42000 by 42 to find how much less than 2200 kcal you have to consume.

42000/42 = 1000
And 2200 -1000 = 1200. Thus, your first answer is the correct one.

... Or, is it? I am writing this while watching a talk show. Go through my reasoning to try to understand why/why not this is correct...
 
Avatrin said:
Hmm.. First we must find the correct equation.

One way to approach this is:

If you remove 700 kcal from your diet, you lose 100 grams.. If you remove 700*60kcal totally over n number of days (with n being sufficiently large), you lose 6kg.. That is 42000 kcal. Our n is equal to 42. Thus, you must divide 42000 by 42 to find how much less than 2200 kcal you have to consume.

42000/42 = 1000
And 2200 -1000 = 1200. Thus, your first answer is the correct one.

... Or, is it? I am writing this while watching a talk show. Go through my reasoning to try to understand why/why not this is correct...
Your whole reasoning is summed up in the first sentence. Your (and mine) calculation is good, but doesn't make the answer correct.

The implicit assumption is that the weight loss (or gain) is proportion to the deficit (or surplus) of calories input.
No it's not. It specifically mentions 'daily input', therefore the meaning is the same... Although only reason why I'd choose 1) over 2) is because 700 kcal is mentioned, and not 1500.