Problem 58 - Prealgebra

Question

Part-time Tuition costs Many two-year colleges have a large number of students who take courses on a parttime basis. Students pay a charge for each credit hour taken plus an activity fee. Suppose the equation \(\$ 1960=\$ 175 x+\$ 35\) can be used to determine the number of credit hours a student is taking during the upcoming semester. Solve this equation.

Step-by-Step Solution

Answer

The student is taking 11 credit hours.

Step 1: Understand the problem

We need to find the number of credit hours, denoted as \(x\), from the given equation \(1960 = 175x + 35\). This equation represents the total cost of tuition, which includes a per-credit charge and an activity fee.

Step 2: Isolate the term with \(x\)

Subtract the activity fee from both sides of the equation to isolate the term involving \(x\). The modified equation will be: \(1960 - 35 = 175x\).

Step 3: Simplify the equation

Calculate the left side to simplify the equation: \(1960 - 35 = 1925\). This results in the equation \(1925 = 175x\).

Step 4: Solve for \(x\)

Divide both sides of the equation by 175 to solve for \(x\): \(x = \frac{1925}{175}\).

Step 5: Calculate the result

Perform the division: \(x = 11\). This represents the number of credit hours the student is taking.

Key Concepts

Solving Equations

Solving equations is a fundamental skill in algebra that requires understanding how to manipulate expressions to find the value of variables. In this situation, the variable represents an unknown quantity—in this case, the number of credit hours a student is taking. When given an equation like \(1960 = 175x + 35\), our goal is to isolate \(x\) on one side of the equation to discover its value.Here's a simplified approach to solving linear equations:

• Begin by identifying the variable you need to solve for.
• Use basic arithmetic operations to manipulate the equation.
• Perform the same operation on both sides of the equation to maintain balance.

When you encounter an equation, start by simplifying it:

• Combine like terms if necessary.
• Move terms that do not include the variable to the opposite side by adding, subtracting, multiplying, or dividing.

In our example, we subtracted \(35\) from both sides to remove the activity fee. This simplified the problem to \(1925 = 175x\). Finally, we divide by \(175\) to find that \(x = 11\). This sequence of steps is universal for solving simple linear equations.

Tuition Calculation

Tuition calculation involves determining the cost a student faces when enrolling in a course or semester of study. The equation provided, \(1960 = 175x + 35\), encapsulates two main components: a cost per credit hour and a fixed activity fee.When you break down tuition fees, it's essential to understand:

• Per credit hour fee: This is the fee associated with each unit of study, represented by \(175x\).
• Activity fee: A fixed fee added to the cost, in this case, \(35\).

The provided equation suggests that the total tuition cost is the sum of these components. It shows that the overall expense can be calculated by multiplying the credit hours \(x\) by the per credit cost, then adding the flat activity fee. This calculation gives a clear picture of how schools bill part-time students.

Credit Hours Calculation

Understanding credit hours calculation is vital for both planning your academic schedule and managing your education expenses. The equation related to this, \(175x\), outlines how tuition correlates to credit hours.Credit hours measure the amount of instruction time a student receives per week during a term. Here's what to know about them:

• A single credit hour typically equals one hour of class time per week.
• Most courses are worth multiple credit hours, influencing both the duration of the course and the cost.
• For part-time students, calculating the total number of credit hours aids in budgeting their tuition effectively.

In our example, solving \(175x + 35 = 1960\) led to finding \(x = 11\), meaning the student is taking 11 credit hours. Understanding this helps students plan their schedule based on personal obligations and financial capabilities.