Problem 1: Evaluating the Initial Inventory
A family stores $150\text{ lbs}$ of rice, $30\text{ lbs}$ of dry beans, and $5\text{ gallons}$ (equivalent to $37.5\text{ lbs}$) of vegetable oil for one person for a full year ($365\text{ days}$).
Calculate the total potential energy content ($E_{total}$) of this entire food system in calories.
Problem 2: The Daily Ration Variable
Using the total calorie archive ($E_{total}$) calculated in Problem 1, compute the actual daily caloric allotment ($C_d$) this inventory provides to the student over a timeframe of $t = 365\text{ days}$. Round your answer to the nearest whole calorie.
Formula Hint: $C_d = \frac{E_{total}}{365}$
Problem 3: Finding the Percentage Deficit
If an active teenager requires an absolute target baseline of $C_{target} = 2,200\text{ calories per day}$ to avoid metabolic starvation, calculate the daily caloric deficit. What percentage of the target daily calorie baseline is missing from the current system?
Problem 4: Modeling a Multi-Person Scaling Variable
Let's correct the inventory so it successfully matches a target baseline of exactly $2,000\text{ calories per person, per day}$.
Write an algebraic formula to calculate the total annual calories required ($E_{family}$) for a family of $P$ people over a year of $365\text{ days}$. Then, calculate the specific value of $E_{family}$ for a family of $P = 4$ people.
Problem 5: Optimizing the Staple Mass Balance
The family decides to balance their $2,000\text{-calorie}$ daily target using a structured weight ratio: **65%** of their daily calories must come from White Rice, and **35%** of their daily calories must come from Dry Beans.
- Calculate how many daily calories must be pulled from Rice, and how many from Beans for one person.
- Using the energy densities given in the instructions, calculate exactly how many pounds of dry rice and how many pounds of dry beans one person needs to store for a full 365-day year. (Round up to the nearest whole pound).
Parent & Educator Evaluation Matrix (Answer Key)
Teachers/Parents: You can print this page out directly or slice this section away before giving the lab assignment to your children.
Problem 1 Answer:
$$\text{Rice: } 150 \times 1,630 = 244,500\text{ kcal}$$
$$\text{Beans: } 30 \times 1,550 = 46,500\text{ kcal}$$
$$\text{Oil: } 37.5 \times 4,000 = 150,000\text{ kcal}$$
$$\text{Total } E_{total} = 244,500 + 46,500 + 150,000 = \mathbf{441,000\text{ total calories.}}$$
Problem 2 Answer:
$$C_d = \frac{441,000\text{ calories}}{365\text{ days}} = \mathbf{1,208\text{ calories per day.}}$$
Parent Note: Emphasize to the student that 1,208 calories is a starvation ration, illustrating why marketing "servings" can be dangerous without looking at the underlying math.
Problem 3 Answer:
$$\text{Daily Caloric Deficit: } 2,200 - 1,208 = 992\text{ calories missing daily.}$$
$$\text{Percentage Deficit: } \frac{992}{2,200} \times 100 = \mathbf{45.1\% \text{ deficit.}}$$
Nearly half of the required survival fuel is completely missing from the target system profile.
Problem 4 Answer:
$$\text{Formula Model: } E_{family} = P \times 2,000 \times 365 \quad \text{or} \quad E_{family} = 730,000P$$
$$\text{For a family of 4: } E_{family} = 4 \times 730,000 = \mathbf{2,920,000\text{ calories.}}$$
Problem 5 Answer:
Step 1 (Daily Caloric Split):
$$\text{Rice: } 2,000 \times 0.65 = 1,300\text{ calories/day} \quad | \quad \text{Beans: } 2,000 \times 0.35 = 700\text{ calories/day}$$
Step 2 (Annual Mass Requirement):
$$\text{Annual Rice Target: } 1,300\text{ kcal/day} \times 365\text{ days} = 474,500\text{ total rice calories needed.}$$
$$\text{Pounds of Rice: } \frac{474,500}{1,630} = 291.1 \rightarrow \mathbf{292\text{ lbs of Rice}}$$
$$\text{Annual Beans Target: } 700\text{ kcal/day} \times 365\text{ days} = 255,500\text{ total bean calories needed.}$$
$$\text{Pounds of Beans: } \frac{255,500}{1,550} = 164.8 \rightarrow \mathbf{165\text{ lbs of Beans}}$$