Solving Linear Word Problems on Work and Wages A linear word problem involves a scenario with two or more unknowns and a linear relationship between the...
Solving Linear Word Problems on Work and Wages
A linear word problem involves a scenario with two or more unknowns and a linear relationship between them. To solve such a problem, we can follow these steps:
Identify the variables: Determine the unknowns that are being measured in the problem. These are usually denoted by variables such as "x," "y," or "w."
Set up a linear equation or inequality: Based on the information provided in the scenario, establish an equation or inequality that relates the variables in a linear fashion. This can be done using variables, expressions, or inequalities.
Solve for the unknown: Rearrange the equation or inequality to isolate the unknown variable on one side of the equation. This will give you the value of the unknown variable.
Check your answer: Substitute the value of the unknown variable back into the original equation or inequality to check if it makes sense and satisfies the conditions of the problem.
Interpret the results: Determine the meaning of the solution in the context of the original problem. This could involve calculating a specific value, comparing it to other values, or making a decision based on the result.
Examples:
Example 1:
John earns $15 per hour and works 40 hours per week. What is his weekly income?
Solution:
Variables: x = hours worked, y = weekly income
Equation: y = 15x
Solution: x = 4, y = $60
Example 2:
Jane earns more than 30 per hour. What is her earning range?
Solution:
Variables: x = hours worked, y = earning range
Inequality: 20 ≤ x ≤ 30
Tips for Solving Linear Word Problems:
Pay attention to the relationships between the variables.
Use algebraic reasoning and logical thinking to solve the problem.
Check your answers to ensure they make sense in the context of the problem.
Practice solving linear word problems to improve your skills