Problem 330 - Elementary Algebra

Question

In the following exercises, solve. Cesar is planning a 4-day trip to visit his friend at a college in another state. It will cost him \(\$ 198\) for airfare, \(\$ 56\) for local transportation, and \(\$ 45\) per day for food. He has \(\$ 189\) in savings and can earn \(\$ 35\) for each lawn he mows. How many lawns must he mow to have enough money to pay for the trip?

Step-by-Step Solution

Answer

Cesar needs to mow 7 lawns.

Step 1 - Calculate total expenses

First, determine the total cost for food by multiplying the daily food cost by the number of days: ewlineCost for food = \ \(45 per day \times 4 days = 180\).

Step 2 - Add all costs

Next, sum up all the expenses: airfare, local transportation, and food. ewlineTotal expenses = \ \(198 (airfare) + 56 (local transportation) + 180 (food) = 434\)

Step 3 - Calculate remaining amount needed

Subtract the amount he already has from the total expenses to find out how much more he needs to earn: ewlineRemaining amount needed = \ \(434 (total expenses) - 189 (savings) = 245\)

Step 4 - Calculate the number of lawns to mow

Divide the remaining amount needed by the amount earned per lawn to determine how many lawns he needs to mow: ewlineNumber of lawns = \ \(245 (remaining amount needed) / 35 (amount earned per lawn) = 7 lawns\)

Key Concepts

Cost Calculation

Planning a trip involves understanding and calculating total costs. Cesar's trip requires adding up various expenses to know how much money he needs. Here's a breakdown:
First, determine costs for each element of the trip. Cesar's expenses include:

• Airfare: \( \$198 \)
• Local transportation: \( \$56 \)
• Food: costs \( \$45 \) per day, over 4 days, so \( 45 \times 4 = \$180 \)

Next, combine these amounts to find the total cost:
Total expenses = \( 198 + 56 + 180 = \$434 \)
This practice helps ensure all expenses are tallied, helping Cesar see the complete picture of his financial needs.

Addition and Subtraction in Algebra

In this word problem, we use addition and subtraction to find out how much more money Cesar needs. He already has some savings, and we'll subtract this amount from his total expenses:

• Total expenses: \( 434 \)
• Savings: \( 189 \)

Remaining amount needed = \( 434 - 189 = \$245 \)
Using addition, we sum up all of Cesar's costs. Using subtraction, we determine what he still needs. This process is essential in budgeting and ensures that you can meet your financial goals.

Division for Problem-Solving

Finally, we use division to figure out how many lawns Cesar needs to mow to make enough money for his trip. We already know how much more he needs (\$245) and how much he earns per lawn (\$35). By dividing the two, we find the answer:

• Remaining amount needed: \( 245 \)
• Amount earned per lawn: \( 35 \)

Number of lawns = \( 245 / 35 = 7 \)
This division step clearly shows us that Cesar needs to mow 7 lawns to reach his financial target. Division helps break down problems into manageable parts, making goals easier to attain.