Question

You have been stranded on a deserted island. On this island are two major food sources; one

that is 80% sugar with a AHxn of -16.2 kJ/g and one that is 65% fats with a AHxn of -37 kJ/g.
Calculate how much of each food source you need to eat to survive if you need 2000 Calories
per day. (*Note Calories listed to survive is nutritional Calories; 1 Calorie is 1 kilocalorie in
reference to nutrition)

Answer 1

To survive on a daily intake of 2000 Calories on a deserted island, you need to calculate the amount of sugar and fats needed. By considering the energy content of each food source, setting up a system of equations, and solving them, you can find the amounts of sugar and fats required to meet the energy requirements.

Step-by-step explanation:

To calculate the amount of each food source needed to survive on a daily intake of 2000 Calories, we need to consider the energy content of each food source.

If a food source is 80% sugar with an AHxn of -16.2 kJ/g, then the energy content per gram of sugar is 0.8 * -16.2 kJ/g = -12.96 kJ/g. Similarly, if a food source is 65% fats with an AHxn of -37 kJ/g, then the energy content per gram of fats is 0.65 * -37 kJ/g = -24.05 kJ/g.

To calculate the amount of each food source needed, we can set up a system of equations based on the energy requirements.

1. Let x be the amount of sugar (in grams) needed.
2. Let y be the amount of fats (in grams) needed.
3. Based on the energy requirements, the total energy from sugar and fats should equal 2000 Calories, which is equivalent to 2000 * 4.18 = 8360 kJ.
4. So, we have the equation: -12.96x - 24.05y = 8360.
5. In addition, we know that x + y = 2000 g, as the total amount of food consumed should be 2000 grams.
6. We can solve this system of equations using substitution or elimination method to find the values of x and y, which will give us the amounts of sugar and fats needed to survive on the deserted island.