A wrestler at a high school in Oklahoma wanted to be a heavy weight wrestler bec

Question

A wrestler at a high school in Oklahoma wanted to be a heavy weight wrestler because his team needs one, but there was a minimum weight of 165 lb, and he only weighed 155 lb. He was taking a chemistry class, so he thought he'd calculate how much sugar he'd have to eat in a month to gain 10 pounds. From combustion data in his chemistry book he found out that most sugars give off 4,000 cal/g of heat from combustion with oxidation, which is what the body does, but in much more controlled chemistry using enzymes. He also looked on the internet and found out that 2,000 calories added to your diet will add a pound of weight. Given he had a month, he figured he needed to add only 670 calories/day or 170 mg of sugar/day, which really confused him. What was his mistake A 12 oz coke has 33 g of sugar, no how many does he have to drink to gain 10 lb The mistake he made is that Calories for food are not the same as calories in chemistry (physics, etc.). Food Calories are really kilocalories (kcal), so he was off by a factor of 1000 on the weight of sugar he needed a day, meaning he needed to consume and extra 170 g of sugar a day, or an extra 5 cokes daily for a month to gain 10 pounds. My calculations are below. NOTE that in the calculation below I use the convention of capitalizing the Calorie unit when it applies to food, ie, really kcal. 10 lbs of weight times 2000 Cal (kcal)/lb is 20,000 Cal (kcal) total over one month. For a 30 day month that is about 670 Cal (kcal)/day. This does agree with wrestlers calculation, if you interpret his calories as food Calories (kcal). That 20,000 Cal (kcal) divided 4 kcal/gram of sugar = 5,000 g of sugar, or 170 g/day. Given a coke contains 33 g of sugar, that's 5 cokes/day. This is 12 oz cokes, not Supper Gulps. Looked at another way, to gain 10 lb takes a total of 150 cokes (or other cans of soda), which about 1 every other day for a year. (One complication in this calculation is that as you gain weight, you need more calories to just maintain your weight If you added a coke a day to your diet and changed nothing else, you will probably gain 5-10 pounds in the first year, but you would level off somewhere.)

Explanation / Answer

The aim is to gain 10 Ib in one month. This can be done by consuming sugar in the form of coke (or any other soda). We need to calculate how many cokes should we consume every day for one month to increase body weight by 10 Ib.
(1) According to wrestler's calculation, 2000 cal of sugar increase bidy weight by 1 Ib. 10 Ib will require 20000 cal. This is to be consumed in 30 days. Hence, each day 20000/30 = 670 cal should be consumed. This corresponds to 670/ (4000)=0.170 g or 170 mg sugar daily for 30 days.
(2) In the above calculation, he made a mistake. He used cal whereas in practice Cal (or kcal) is used. 1 Cal = 1 kcal = 1000 cal.
2000 Cal of sugar increase bidy weight by 1 Ib. 10 Ib will require 20000 Cal. This is to be consumed in 30 days. Hence, each day 20000/30 = 670 Cal should be consumed. This corresponds to 1000*670/ (4000)=170 g mg sugar daily for 30 days.
A coke contains 33 g of sugar. Hence, 170/33 = 5 cokes everyday for 30 days will increase the body weight by 10 Ib.

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