In Exercises 36–43, use the five-step strategy for solving word problems. An apartment complex has offered you a move-in special of 30% off the first month's rent. If you pay $945 for the first month, what should you expect to pay for the second month when you must pay full price?

Verified step by step guidance

1. Step 1: Understand the problem. You are given that the first month's rent is $945, which is 30% off the full price. You need to find out what the full price is.
2. Step 2: Translate the problem into a mathematical equation. Let's denote the full price as 'x'. The first month's rent is 70% of the full price, because you got a 30% discount. So, we can write the equation as 0.7x = $945.
3. Step 3: Solve the equation. To find 'x', you need to divide both sides of the equation by 0.7.
4. Step 4: Check your solution. Substitute 'x' back into the equation to make sure it equals $945.
5. Step 5: Answer the question. The value of 'x' is the full price you should expect to pay for the second month.

Key Concepts

Percentage Calculation

Percentage calculation involves determining a portion of a whole expressed as a fraction of 100. In this problem, the 30% discount on the first month's rent means you will pay only 70% of the original rent. Understanding how to calculate percentages is crucial for determining the actual amount paid after applying the discount.

Solving for Original Price

To find the original price before the discount, you can set up an equation based on the discounted price. If $945 represents 70% of the original rent, you can use the formula: original rent = discounted price / (1 - discount rate). This step is essential to determine what the full rent will be for the second month.

Understanding Word Problems

Word problems require translating a real-world scenario into mathematical expressions or equations. This involves identifying key information, such as the discount rate and the amount paid, and determining what is being asked. Mastering this skill is vital for effectively applying mathematical concepts to solve practical problems.