Henry shows potential cities he could visit, as well as what he estimates it will cost him to visit each one. All costs are given in grazilian reals (RS).
| City | Cost (RS) |
| ---------------- | --------- |
| Salvador | 224 |
| Duque de Caxias | 242 |
| Rio de Janeiro | 193 |
| Campinas | 185 |
| Porto Alegre | 153 |
| Guarulhos | 120 |
| Fortaleza | 201 |
Henry's original plan was to visit Duque de Caxias, Campinas, Rio de Janeiro, and Guarulhos. However, he only has R$699 to spend, so he cannot afford to use his original itinerary. Which of the following changes will be the cheapest swap Henry can make and still come in under budget?
A. Replace Duque de Caxias with Salvador.
B. Replace Duque de Caxias with Fortaleza.
Answer (2)
Henry's cheapest swap option to stay within his budget is to replace Duque de Caxias with Fortaleza, bringing his total cost to exactly RS 699. Therefore, the answer is option B.
;
Calculate the original cost: 242 + 185 + 193 + 120 = 740 .
Calculate the cost of option a: 224 + 185 + 193 + 120 = 722 .
Calculate the cost of option b: 201 + 185 + 193 + 120 = 699 .
Option b is the cheapest swap within budget: b .
Explanation
Analyzing the Problem Let's analyze Henry's travel plans to see which option fits his budget.
Calculating Original Cost First, we need to calculate the cost of Henry's original plan, which includes Duque de Caxias, Campinas, Rio de Janeiro, and Guarulhos. The costs are RS 242, RS 185, RS 193, and RS 120, respectively. So the total cost is: 242 + 185 + 193 + 120 = 740 Since Henry only has RS 699, his original plan is too expensive.
Evaluating Option A Now, let's evaluate option a, where Henry replaces Duque de Caxias (RS 242) with Salvador (RS 224). The new cost would be: 224 + 185 + 193 + 120 = 722 This option costs RS 722, which is still over Henry's budget of RS 699.
Evaluating Option B Next, let's evaluate option b, where Henry replaces Duque de Caxias (RS 242) with Fortaleza (RS 201). The new cost would be: 201 + 185 + 193 + 120 = 699 This option costs RS 699, which is exactly Henry's budget.
Determining the Cheapest Swap Since option a is over budget and option b is exactly on budget, option b is the only viable option. Therefore, the cheapest swap Henry can make and still stay within budget is to replace Duque de Caxias with Fortaleza.
Examples
This problem demonstrates how to manage a budget when planning a trip. By comparing costs and making strategic substitutions, you can optimize your itinerary to fit within your financial constraints. This type of problem-solving is useful in many real-life scenarios, such as planning events, managing projects, or even grocery shopping, where you need to make choices based on a limited budget. For instance, if you have a budget of $100 for groceries and you want to buy certain items, you might need to swap out more expensive items for cheaper alternatives to stay within your budget.
