Math Problem Statement
solve
Solution
Let's solve the problem step by step.
Problem Summary:
- The first mechanic charges $45/hour.
- The second mechanic charges $80/hour.
- Combined, they worked for 20 hours.
- They earned a total of $1,425.
- Find how many hours each mechanic worked.
Define Variables:
Let:
- = hours worked by the first mechanic.
- = hours worked by the second mechanic.
Equations:
- Total hours:
- Total earnings:
Solve the System of Equations:
From Equation (1):
Substitute into Equation (2):
Substitute into Equation (1):
Solution:
- The first mechanic worked 5 hours.
- The second mechanic worked 15 hours.
Would you like a detailed breakdown or have additional questions? Here are some related questions to explore further:
- What if the hourly rates were swapped? How would the solution change?
- How would you graphically represent this system of equations?
- What happens if the total hours worked were different but earnings stayed the same?
- Can you verify the solution by checking total earnings for the two mechanics?
- How can this system of equations be solved using matrices?
Tip: Always double-check your solution by substituting values back into the original equations!
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Algebra
Systems of Linear Equations
Formulas
x + y = Total Hours
45x + 80y = Total Earnings
Theorems
Substitution Method for Solving Systems of Equations
Suitable Grade Level
Grades 8-10
Related Recommendation
Solving Systems of Linear Equations: Mechanics' Hourly Rates
Find Hourly Rates for Two Mechanics Using System of Linear Equations
Solve System of Equations: When Two Plumbers Charge the Same
System of Equations to Determine Hours Worked by Justin and Daniel
Solve a System of Linear Equations: Mike's Weekly Hours and Pay