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. Define the variables: Let the full price of the rent be represented by 'x'. The first month's rent is 30% off, meaning you pay 70% of the full price.
2. Set up the equation for the first month's rent: Since 70% of the full price is \$945, write the equation as 0.7 * x = 945.
3. Solve for 'x': Divide both sides of the equation by 0.7 to isolate 'x'. This will give you the full price of the rent.
4. Interpret the result: The value of 'x' represents the full price of the rent, which is the amount you will pay for the second month since there is no discount.
5. Conclude: Once you have the value of 'x', you know the second month's rent is equal to the full price, as no discount applies.

Key Concepts

Percentage Calculation

Understanding percentages is crucial for solving problems involving discounts or increases. In this scenario, the apartment complex offers a 30% discount on the first month's rent. To find the original rent before the discount, one must calculate what amount corresponds to 70% of the original price, as 100% minus 30% equals 70%.

Algebraic Representation

Using algebraic expressions allows for a clearer representation of relationships between quantities. In this problem, if we let 'x' represent the original rent, we can set up the equation 0.7x = 945 to find the full price of the rent. This approach simplifies the process of solving for unknowns in word problems.

Understanding Full Price vs. Discounted Price

Differentiating between full price and discounted price is essential in financial problems. The first month's rent is paid at a discounted rate, while subsequent months require payment at the full price. Recognizing this distinction helps in calculating future payments accurately, as the second month's rent will be the original price determined from the first month's calculations.