Math Problem Statement

A set of problems involving hourly wages, weekly pay, overtime, and mileage pay for different individuals across various professions. Each problem asks for the calculation of either total pay or the number of hours worked, using given rates and overtime rules.

Solution

Let's go over the questions one by one and solve them:

1. Ronaldo Scanlon is a financial consultant. He earns $30 per hour and works 32.5 hours a week. What is his weekly pay?

  • Formula: Weekly Pay = Hourly Rate × Hours Worked
  • Solution:
    30(per hour)×32.5hours=975USD30 \, \text{(per hour)} \times 32.5 \, \text{hours} = 975 \, \text{USD}

Ronaldo's weekly pay is $975.


2. Elaine Mellon earns $17.80 per hour as an electronic billing specialist for a legal clinic. How many hours per week must she work if she wants to earn approximately $675.00 per week?

  • Formula: Hours Worked = Total Weekly Earnings ÷ Hourly Rate
  • Solution:
    675÷17.80=37.92hours675 \div 17.80 = 37.92 \, \text{hours}

Elaine must work approximately 37.92 hours per week.


3. Bobby Hsu is an office manager at a weekly newspaper. He earns $22.50 per hour. How many hours per week does Bobby work if he earns $522.00 per week?

  • Formula: Hours Worked = Total Weekly Earnings ÷ Hourly Rate
  • Solution:
    522÷22.50=23.2hours522 \div 22.50 = 23.2 \, \text{hours}

Bobby works approximately 23.2 hours per week.


4. Lauren Rodriguez earns $8.35 per hour as a swimming instructor. How many hours per week must she work if she wants to earn approximately $190.00 per week?

  • Formula: Hours Worked = Total Weekly Earnings ÷ Hourly Rate
  • Solution:
    190÷8.35=22.75hours190 \div 8.35 = 22.75 \, \text{hours}

Lauren must work approximately 22.75 hours per week.


5. Rick Haskins is paid $18 an hour as a pastry chef for a regular 35-hour week. His overtime rate is 1.5 times his regular hourly rate. This week, he worked his regular 35 hours plus 8 hours of overtime. What is Rick's total pay?

  • Formula:
    Regular Pay = Regular Hours × Regular Rate
    Overtime Pay = Overtime Hours × Overtime Rate (1.5 × Regular Rate)
    Total Pay = Regular Pay + Overtime Pay
  • Solution:
    Regular Pay = 35×18=630USD35 \times 18 = 630 \, \text{USD}
    Overtime Pay = 8×(1.5×18)=8×27=216USD8 \times (1.5 \times 18) = 8 \times 27 = 216 \, \text{USD}
    Total Pay = 630+216=846USD630 + 216 = 846 \, \text{USD}

Rick's total pay is $846.


If you'd like me to continue with the rest of the questions or need more detailed explanations, let me know!

Here are 5 related questions to expand your understanding:

  1. What would happen if Elaine wanted to earn $800 instead of $675? How many hours would she work?
  2. If Lauren worked 25 hours instead of 22.75, what would her weekly earnings be?
  3. What is the formula for calculating overtime pay when overtime hours and the rate are given?
  4. How would Rick's total pay change if he worked 10 hours of overtime instead of 8?
  5. What is the percentage increase in Rick's pay due to his overtime hours?

Tip: When calculating weekly pay, ensure that you include overtime rates correctly for any hours worked beyond regular working hours.

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Math Problem Analysis

Mathematical Concepts

Algebra
Arithmetic
Overtime Calculation
Rate and Time

Formulas

Weekly Pay = Hourly Rate × Hours Worked
Overtime Pay = Overtime Hours × Overtime Rate
Total Pay = Regular Pay + Overtime Pay
Hours Worked = Total Earnings ÷ Hourly Rate
Mileage Pay = Rate per Mile × Total Miles

Theorems

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Suitable Grade Level

Grades 7-10