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Math problem set Grade 9 Careers & CTE

Bramstead Utility: What a Class II License Costs and Returns

Ten grade 9 careers problems following a fictional operator-in-training through course fees, study hours, a wage step, and the months it takes to earn the cost back.

Objectives

  1. Students will calculate annual pay, a wage step, and its percent increase from an hourly rate.
  2. Students will total the money and time costs of earning an operator license, including tuition reimbursement.
  3. Students will solve for the number of months a wage step needs to repay the cost of earning a license.

Vocabulary

Key words: operator in training, wage step, tuition reimbursement, contact hours, opportunity cost, shift differential

Teacher overview

Devorah works as an operator in training at the fictional Bramstead Utility District and wants the Class II license that would move her into a full operator position. This set follows one decision from end to end: what the license costs in fees, what it costs in hours, what the wage step is worth, and how long the step takes to repay the cost. The numbers price one route into the work, and a certificate or a degree route would need its own accounting with its own tuition, timeline, and pay, so students should read the result as a method rather than a verdict on which path is better. The error this set is built to catch is a payback calculation that counts only the fees. Students divide the $465 net fee cost by the monthly raise, get an answer under a month, and conclude that licensing is nearly free, when the 132 hours Devorah spends in class and studying are the larger part of what she gives up.

Bramstead Utility: What a Class II License Costs and Returns — Grade 9 Careers & CTE
Name: ____________________________ Date: ______________

Problems

Use the following information about the fictional Bramstead Utility District for every problem. All figures are set for this scenario. Write the unit beside every number you calculate, and round money to the nearest cent and other answers to one decimal place.

  • Devorah earns $22.40 per hour as an operator in training.
  • A Class II operator at Bramstead earns $27.10 per hour.
  • Full-time work at Bramstead is 2,080 hours per year.
  • The exam preparation course costs $650 in tuition and meets for 48 contact hours.
  • The state charges a $145 exam fee and a $60 application fee.
  • Bramstead reimburses 60 percent of course tuition, but only after the employee passes the exam.
  • Devorah plans to study 6 hours per week for 14 weeks, on top of the course's contact hours.
  • Bramstead pays a shift differential of $1.15 per hour for hours worked on the night shift.
  1. Devorah earns $22.40 per hour and works 2,080 hours per year. Calculate her annual pay as an operator in training.
  2. A Class II operator at Bramstead earns $27.10 per hour for the same 2,080 hours per year. Calculate the annual pay of that position.
  3. Using the annual pay of $46,592 for an operator in training and $56,368 for a Class II operator, calculate the raise the license would bring in one year.
  4. Using an annual raise of $9,776 against a starting annual pay of $46,592, calculate the percent increase.
  5. Devorah pays $650 in tuition, a $145 exam fee, and a $60 application fee. Calculate what she pays out of pocket before any reimbursement.
  6. Bramstead reimburses 60 percent of the $650 tuition after she passes. Starting from total out-of-pocket costs of $855, calculate her net cost after the reimbursement arrives.
  7. The course meets for 48 contact hours, and Devorah plans to study 6 hours per week for 14 weeks. Calculate the total hours the license will take.
  8. Devorah's time is worth her current wage of $22.40 per hour. Using a total of 132 hours, calculate the value of the time she spends earning the license.
  9. Devorah's total cost is her net cost of $465 plus the $2,956.80 value of her time. Her annual raise of $9,776 arrives in equal monthly amounts. Write and solve an equation for the number of months of raise needed to cover the total cost.
  10. As a Class II operator earning $27.10 per hour, Devorah expects to work 1,040 of her 2,080 hours on the night shift, which pays a shift differential of $1.15 per hour. Calculate the differential pay she would earn in a year.

From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.

Answer Key
  1. Answer: $46,592.
    Multiply the hourly rate by the annual hours: $22.40 per hour times 2,080 hours equals $46,592 per year.
  2. Answer: $56,368.
    Multiply the hourly rate by the annual hours: $27.10 per hour times 2,080 hours equals $56,368 per year.
  3. Answer: $9,776.
    Subtract the smaller annual pay from the larger: $56,368 minus $46,592 equals $9,776 per year.
  4. Answer: 21.0 %.
    Divide the raise by the starting pay, then multiply by 100: $9,776 divided by $46,592 equals 0.2098, and times 100 gives 20.98 percent, which rounds to 21.0 percent.
  5. Answer: $855.
    Add the three amounts: $650 plus $145 plus $60 equals $855.
  6. Answer: $465.
    The reimbursement is 60 percent of the $650 tuition, which is 0.60 times $650, or $390. Subtract it from the total: $855 minus $390 equals $465.
  7. Answer: 132 hours.
    Study time is 6 hours per week times 14 weeks, which equals 84 hours. Add the course contact hours: 84 hours plus 48 hours equals 132 hours.
  8. Answer: $2,956.80.
    Multiply the hours by her wage: 132 hours times $22.40 per hour equals $2,956.80.
  9. Answer: 4.2 months.
    The total cost is $465 plus $2,956.80, which equals $3,421.80. The monthly raise is $9,776 divided by 12 months, which equals $814.67 per month. Let m be the number of months, so $814.67 times m equals $3,421.80. Dividing gives m equal to 4.2 months.
  10. Answer: $1,196.
    Multiply the night hours by the differential: 1,040 hours times $1.15 per hour equals $1,196 per year.

Differentiation

Support

Give these students a table with the first column filled in, listing each fictional Bramstead figure beside the problem that uses it, so the work begins at the arithmetic rather than at finding the number. Work problem 1 aloud with the class, writing the units in the multiplication, then let students mirror that setup in problem 2. For problem 9, provide the equation with the blank already placed, so students solve rather than build it.

Extension

Ask these students to redo problem 9 on the assumption that Devorah fails the exam on the first attempt, pays the $145 exam fee a second time, receives no tuition reimbursement until she passes, and spends another 20 hours studying. Then have them state, in one sentence, which of the three added costs moves the payback period most and why.

ELL supports

Pre-teach wage step, tuition reimbursement, contact hours, shift differential, opportunity cost, and payback with a simple timeline of the fictional Devorah's year, marking the course, the exam, and the first paycheck at the new rate. Supply a two-column glossary card pairing each term with the number in the problem set that measures it. Allow solutions to be written as labeled arithmetic rather than sentences.

Extensions

Have students look up the current fee schedule and experience requirements published by their own state's drinking water operator certification program, then rebuild problems 5, 6, and 9 with those real figures and whatever starting wage a local posting shows. Comparing their result against the fictional Bramstead answer shows how much the payback period depends on local wages rather than on the fees themselves.