Problem 12 - Algebra 1

Question

Find the unit rate. \(\$ 121.50\) for working 18 hours

Step-by-Step Solution

Answer

The unit rate is \$6.75 per hour

Step 1: Identify the Total Pay and Total Hours

The total pay for 18 hours of work is \$121.50 and the total hours worked is 18.

Step 2: Apply the Formula for Unit Rate

The formula to calculate unit rate is to divide the total pay by the total number of hours. In this case, divide \$121.50 by 18.

Step 3: Calculate the Unit Rate

After dividing \$121.50 by 18, the unit rate is \$6.75 per hour.

Key Concepts

Unit Rate Calculation

Understanding the process of calculating the unit rate is crucial for everyday life and in various academic fields. Simply put, a unit rate tells you how much of something you get for one unit of another thing. For example, if you are told that a car travels 300 miles on 15 gallons of fuel, the unit rate is the number of miles the car can travel per gallon of fuel.

To find the unit rate, you divide the first quantity by the second. In our textbook example, we have a total pay of \(\$121.50\) for working 18 hours. By applying the unit rate formula, which is to divide the total pay by the total hours (\(\$121.50 \/ 18\)), we arrive at \(\$6.75\). This result means the worker earns \(\$6.75\) for every hour worked. It's a straightforward yet powerful tool for comparing rates and costs in various situations, such as determining the best buy between different products when shopping or comparing job offers.

Algebraic Expressions

Algebraic expressions are the backbone of algebra and provide a way to represent real-world problems mathematically. An algebraic expression is a combination of numbers, variables, and arithmetic operations (such as addition, subtraction, multiplication, and division). For example, the unit rate calculation can be represented by an algebraic expression, such as \(\frac{Total\ Pay}{Total\ Hours}\), highlighting the division operation.

Understanding how to work with these expressions is critical since they allow us to describe relationships and changes. To simplify or evaluate an algebraic expression, we combine like terms and use the order of operations (PEMDAS/BODMAS rules). Breaking down complex scenarios into algebraic expressions, and manipulating them to find a solution, is a fundamental skill in problem solving in algebra.

Problem Solving in Algebra

Problem solving in algebra involves the application of various strategies to solve equations and find unknown values. It typically requires identifying the problem, planning a method of solution, carrying out the plan, and then evaluating the result. In our unit rate calculation, the core problem is determining the amount earned per hour. We translated the given information into a mathematical model using an algebraic expression and then solved it using straightforward arithmetic division.

This type of algebraic thinking is immensely useful in a wide range of fields, from economics to engineering. The systematic approach to solving such problems fosters critical thinking and can be applied not just in mathematics, but in real-life situations as well. Remember, practice is key in honing problem-solving skills in algebra, as well as getting comfortable with common algebraic operations, and solving problems efficiently.