Problem 11 - Algebra and Trigonometry

Question

The bus fare in a city is \(\$ 1.25 .\) People who use the bus have the option of purchasing a monthly discount pass for \(\$ 15.00 .\) With the discount pass, the fare is reduced to \(\$ 0.75 .\) Determine the number of times in a month the bus must be used so that the total monthly cost without the discount pass is the same as the total monthly cost with the discount pass.

Step-by-Step Solution

Answer

The bus must be used 30 times in a month for the total monthly cost with the discount pass to be the same as the total monthly cost without the discount pass.

Step 1: Define the Variables

Let 'x' represent the number of times the bus is used in a month. The monthly cost with the discount pass is \(15.00 + 0.75x\) and the monthly cost without the discount pass is \(1.25x\).

Step 2: Set Up the Equation

Since the problem states that the total cost with the pass is equal to the total cost without the pass, we set both expressions equal to each other resulting in the following equation: \[15.00 + 0.75x = 1.25x\]

Step 3: Solve the Equation

To solve the equation, isolate 'x'. First, subtract \(0.75x\) from both sides to get \[15.00 = 0.50x\]Now, divide both sides by 0.50 to find 'x': \[x = 15.00 / 0.50 = 30\]