Final answer:
To write a budget constraint equation representing the scenario of a family's spending on housing and food, you take into account the price of food per meal and the total number of meals consumed. The equation 120P + H = B, where P is the price per meal, H is the housing cost, and B is the total budget, captures this relationship.
Step-by-step explanation:
Writing a Budget Constraint Equation
Let P be the price of food for each person. If we examine the provided scenario where a family has a certain budget that they can spend on housing and food, we can develop a budget constraint equation.
Specifically, let's consider a point, say point B, where each of the four persons eats one meal each day for a month. This equals 120 meals over 30 days. If each meal costs P dollars, then the total spending on food (F) is 120P.
Consequently, if the family has a budget (B) and they spent $292 on food, they are left with $940 for housing, which can afford a 470 square foot studio apartment. The equation for the budget constraint based on the provided details would thus look like this:
F + H = B
Where F is the total spending on food, H is the spending on housing, and B is the total budget. Using the values from point B:
120P + H = B
This equation simplifies the relationship between food prices, quantity, and budget, much like Alphonso's case of balancing the cost of burgers and bus tickets within his budget.