Question

Suppose Becky has a budget of $32 that she spends on movies (Q 1 ​ ) and roller skating (Q 2 ​ ). The price of movie tickets recently increased from $5 per person to $8 per person, and the price of roller skating decreased from $5 to $4 per p What is Becky's new budget constraint?

Answer 1

Answer: Let's assume Becky's budget is allocated as follows:

x: Quantity of movies (Q1)

y: Quantity of roller skating (Q2)

p1: Price of movies per person

p2: Price of roller skating per person

B: Budget

Given the following information:

Initial price of movies (p1) = $5 per person

Updated price of movies (p1') = $8 per person

Initial price of roller skating (p2) = $5 per person

Updated price of roller skating (p2') = $4 per person

Initial budget (B) = $32

We can calculate the maximum quantities of movies and roller skating using the formula:

Q1 = (B / p1') - (p2' / p1') * Q2

Q2 = (B / p2') - (p1' / p2') * Q1

Let's substitute the given values into the formula:

Q1 = (32 / 8) - (4 / 8) * Q2

Q2 = (32 / 4) - (8 / 4) * Q1

Simplifying the equations, we get:

Q1 = 4 - 0.5 * Q2

Q2 = 8 - 2 * Q1

These equations represent Becky's new budget constraint, considering the updated prices of movies and roller skating.

Answer 2

8Q1 +4Q2 ≤ 32

Explanation:

You want to know Becky's budget constraint if she has a budget of $32 that she spends on Q1 movies at $8 each, and Q2 roller skating tickets at $4 each.

Spending

Becky's spending will be the sum of the costs of movie tickets and skating tickets. Each of those costs is the product of the ticket price and the number of tickets.

movie cost + skating cost ≤ ticket budget

8Q1 +4Q2 ≤ 32

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