Salaries

“Never confuse the size of your paycheck with the size of your talent.”

Marlon Brando (actor)

Salaries Annual Salary1) Set Salary2) No overtime3) Benefits4) Vacation

Hourly Pay1) Salary changes

every week2) Overtime pay3) Benefits for full time4) No vacation

Carpenter - $52,880 Garbage Man - $37,100 High School Teacher - $61,470 Financial Analyst - $93,760 Police Officer - $55,580 Fire Fighter - $48,140 Dentist - $169,340 Pediatrician - $159,390

Massachusetts Department of Labor website

Average Salaries

Weekly◦52 Paychecks → Annual Salary ÷ 52

Bi-Weekly◦26 Paychecks → Annual Salary ÷ 26

Semi-Monthly◦24 Paychecks → Annual Salary ÷ 24

Monthly◦12 Paychecks → Annual Salary ÷ 12

Pay Periods Page 300, 2-10

Christina is paid biweekly. Her annual salary is

$37,000. What is her biweekly salary, rounded

to the nearest cent?

→ Biweekly = 26 paychecks

Biweekly Salary = annual salary ÷ # of paychecks

= $37,000 ÷ 26

= 1423.0769

= $1,423.08

Mr. Varello is paid semimonthly. His annual salary is $64,333. What is his semimonthly salary, rounded to the nearest cent?

→ Semimonthly = 24 paychecks

Salary = annual salary ÷ # of paychecks

= $64,333 ÷ 24

= 2680.5416 = $2,680.54

Manny is paid semimonthly. His semimonthly salary is $1,239. What is his annual salary?

How many paychecks does Manny get?→ 24 paychecks

How much is each paycheck for?→ $1,239

How much does Manny receive per year?→24 paychecks x $1,239

= $29,736

Please do problems 2-10 in your notebook on page 300 of the textbook. Show all work.

Classwork

Hourly Rate

Sarah has been offered a new job as an assistant manager in a shoe department.

She will work 54 hours each week and earn $15

an hour. For this work schedule and rate of pay, is it possible for Sarah’s gross pay for one month to be at least $3,650?

Think about this…

Typical work week is 40 hours◦ Workers receive regular pay for up to 40 hours per

week

To calculate pay for regular hours:

◦ Wage = (hourly rate) x (number of hours worked)

Regular Time

Maureen works at a local Chicken King Restaurant. Her regular hourly wage is $9.70. If she regularly works 40 hours per week, what is her regular weekly pay?

Weekly Pay= (hourly rate) x (number of hours)

= (9.70) x (40) = 388

Maureen makes $388 per week

Example:

Mark Willow works as a customer service representative and is paid $9.10 per hour. He worked 38 hours lat week. What was his gross pay?

Gross pay = (hourly rate) x (number of hours)

= (9.10) x (38) = 345.8

Mark earned $345.80 last week

Try it…

Hours worked in a week greater than 40

Usually pays 1.5 times hourly rate “Time and a half”

How many hours of overtime for:◦ 45 hours?◦ 54 hours?◦ 38 hours?

Overtime

Janice earns $10 per hour. If her regular hours are 40 hours per week, and she receives time-and-a-half overtime, find her total pay for a week in which she works 45 hours.

Total Pay = Regular Pay + Overtime Pay

Example:

Calculating Pay

Reg Pay = $400 OT Pay = $75

Regular Pay

(Reg. Hrs) x (Hrly Rate) (40 hours) x ($10)

= $400

Overtime Pay

(OT hrs)x(hrly rate)x(1.5)

(5 hrs) ($10) (1.5)

= $75

Janice earns $10 per hour. If her regular hours are 40 hours per week, and she receives time-and-a-half overtime, find her total pay for a week in which she works 45 hours.

Total Pay = Regular Pay + Overtime Pay

Total Pay = $400 + $75

= $475

Example:

Kenny Walker works as a shopping mall security guard and is paid $7.50 an hour. He is paid time-and-a-half for all hours over 40. Find his gross pay when he works 46 hours a week.

Gross Pay = Reg. Pay + OT Pay = $300 + $67.50

= $367.50

Try it…

Sarah has been offered a new job as an assistant manager in a shoe department.

She will work 54 hours each week and earn $15

an hour. For this work schedule and rate of pay, is it possible for Sarah’s gross pay for one month to be at least $3,650?

Yes, gross pay would be:

Think about this…

$3,660

Page 301, numbers 12-21

For double time, multiply by 2 instead of 1.5

Classwork

2) Yoko is paid semimonthly. How many fewer paychecks does she receive in a year compared to someone who is paid weekly?

28 paychecks

Homework Answers

3) Sean is paid biweekly. His annual salary is $42,500. What is his biweekly salary to the nearest cent?

$1,634.62

Homework Answers

4) Cynthia’s semimonthly salary is $1,371.50. What is her annual salary?

$32,916

Homework Answers

5) Baseball player Alex Rodriguez earned $27,708,525 in 2007. He played in 158 games. What was his salary per game to the nearest thousand dollars?

$175,370.41

$175,000

Homework Answers

6) Ceil gets paid biweekly. Her biweekly salary is $1,763.28. What is her annual salary?

$45,845.28

Homework Answers

7) John’s weekly salary is $478.25. His employer is changing the pay period to semimonthly.

What is John’s annual salary? $24,869

What will John’s semimonthly salary be? $1,036.21

Homework Answers

8) Ralph earns $72,000 annually and is paid semimonthly. Alice also earns $72,000 but is paid biweekly.

How many more paychecks does Alice get? 2 paychecks

What is the difference between Ralph and Alice’s paycheck?

$230.77

Homework Answers

9) Beth’s annual salary was $38,350. This year she received $46,462. Beth is paid biweekly.

What was her biweekly salary last year? $1,475

What is Beth’s biweekly salary this year? $1,787

How much more does Beth receive? $312

Homework Answers

10) Justin is a golf pro. He works eight months per year, and is paid $76,000. During the winter months, he teaches golf privately and earns another $12,500. What is his average salary based on his yearly earnings?

$7,375

Homework Answers

12) Hector works in a gas station and earns $8.60 per hour. Last week he worked 29 hours. What was his gross pay?

$249.40

Homework Answers

13) Eddie works at a Beep-N-Kleen car wash. He earns $8.40 per hour. Last week he worked x hours. What was his gross pay?

$8.40x

Homework Answers

14) Lynn makes $9 an hour. Last week she worked 43 hours.

What was her regular gross pay? $360.00

What was her overtime pay? $40.50

What was her total pay? $400.50

Homework Answers

15) Amy works 20 per week. She earns $8.10 per hour and receives double-time for working on Sundays. Next week, she will work 20 regular hours and 8 hours on Sunday. What will her total pay be?

$291.60

Homework Answers

16) Tom earns $12.50 per hour. He regularly works 40 hours a week and receives time-and-a-half for overtime. Last week he worked 42 hours. How much did he make?

$537.50

Homework Answers

17) Pedro works 35 regular hours per week. He earns $9.20 per hour and time-and-a-half for overtime. Last week he worked 41 hours and received a gross pay of $305.80, which was incorrect. How much is he owed?

$99.00

Homework Answers

18) Colby and Cheryl work in different supermarkets. Colby earns $8.90 an hour and is paid time-and-a-half for overtime. Cheryl earns $7.10 an hour and is paid double time. Who earns more for one hour of overtime?

Cheryl by 85 cents

Homework Answers

19) Ron earns x dollars per hour. He works 40 hours per week. What is his annual salary?

52 (40x)

Homework Answers

20) Michael earns $10 an hour. He works 40 hours per week. How many overtime hours would he need to work for his overtime pay to be greater than he regular pay?

27 hours

Homework Answers

21) Jim worked 40 hours last week plus 8 overtime hours. His gross pay was $1,248.

What was his hourly rate? $24

What was his overtime hourly rate? $36

Homework Answers

Algebraic Expressionsand Salaries

Equations involving 1 or more variables

Can use any letter to represent a variable

Similar to what we have been doing.

Algebraic Expressions

Christina is paid biweekly. Her annual salary is $37,000. What is her biweekly salary, rounded to the nearest cent?

Biweekly Salary =

Annual Salary =

# of Paychecks =

paychecks of #

salary annual

$37,000

26

26

$37,000 $1,423.08

Example 1

Christina is paid biweekly. Her annual salary is $Y. What is her biweekly salary, rounded to the nearest cent?

Biweekly Salary =

Annual Salary =

# of Paychecks =

paychecks of #

salary annual

$Y

26

26

$Y

Example 1 - Algebraic

26

Y

Manny is paid semimonthly. His semimonthly salaryis $1,239. What is his annual salary?

Annual Salary =

Semimonthly salary =

# of Paychecks =

$1,239

24

Example 2

(salary ) (# of paychecks)

= ($1,239) (24) = $29,736

Carlos earns x dollars biweekly. Express his annual salary algebraically.

Annual Salary =

Biweekly salary =

# of Paychecks =

$x

26

Example 2 - Algebraic

(Biweekly salary ) (# of paychecks)

= ($x) (26) = 26x

Slide 47

Alex is paid semimonthly. His annual salary is y dollars. Express his semimonthly salary algebraically.

Annual Salary = $Y

Paid Semimonthly

Semimonthly Salary =

CHECK YOUR UNDERSTANDING

What does this mean?

What does this mean?

Alex makes $Y per year

Alex gets 24 paychecks

24

y

Maureen works at a local Chicken King Restaurant. Her regular hourly wage is $9.70. If she regularly works 40 hours per week, what is her regular weekly pay?

Weekly Pay= (hourly rate) x (number of hours)

= (9.70) x (40) = 388

Maureen makes $388 per week

Example 3

Roger regularly works h hours per week at a rate of d dollars per hour. Express his annual salary algebraically.

Weekly Pay= (hourly rate) x (number of hours)

Example 3 - Algebraic

= ($d) (h hours)= d • h dollars per week

Annual Salary = (weekly salary) (52)

= 52dh

Janice earns $10 per hour. If her regular hours are 40 hours per week, and she receives time-and-a-half overtime, find her total pay for a week in which she works 45 hours.

Total Pay = Regular Pay + Overtime Pay

Total Pay = (40)($10)

= $475

Example 4

+ (5)($10)(1.5)

Ron regularly works 40 hours per week, at a rate of x dollars per hour. Last week he worked y overtime hours at time-and-a-half. Express his total weekly salary algebraically.

Total Pay = Regular Pay + Overtime Pay

Total Pay =

Example 4 - Algebraic

+ (y)(x)(1.5)

(reg hrs)(hrly rate)+ (ot hrs)(hrly rate)(1.5)

= 40x

= 40x + 1.5xy

Mr. Whittaker earns b dollars biweekly. What is his annual salary?

Annual salary = (biweekly salary)(# of paychecks)

= (b) (26)

= 26b

Homework Problem 1

His employer is changing the pay procedure to monthly, but no annual salaries are changing. What is his monthly salary?

Monthly salary =

Homework Problem 1

paychecks of #

salary annual

= 26b12

Ms. Saevitz is paid semimonthly. Her annual salary is a dollars. What is Ms. Saevitz’s semimonthly salary?

Semimonthly salary =

Homework Problem 2

paychecks of #

salary annual

= a24

If her office changes to a biweekly pay schedule, what will Ms. Saevitz’s biweekly salary be?

Biweekly salary =

Homework Problem 2

paychecks of #

salary annual

= a26

Mr. Lewis regularly works h hours per week at a rate of y dollars per hour. Express his annual salary in terms of h and y.

Weekly Salary = hy

Annual Salary = 52hy

Homework Problem 3

If you earn d dollars per hour regularly, express your hourly overtime rate algebraically if you are paid time-and-a-half for overtime.

Overtime Rate = 1.5d

Homework Problem 4

Mrs. Trobiano regularly works 40 hours per week at a rate of d dollars per hour. Last week she worked h overtime hours at double time. What was her total salary in terms of d and h.

Reg. Pay = 40dOt Pay = hd(2)

Total Pay = 40d + 2hd

Homework Problem 5

You work at a store making d dollars per hour. Last week, you worked 35 regular hours and h overtime hours, at time-and-a-half. Write a formula that expresses your weekly pay.

Weekly Pay = 35d + hd(1.5)

= 35d + 1.5hd

Writing Formulas

Last week, you worked a total of 52 hours, 40 of which were regular hours. You are paid x dollars per hour and are paid double time for all overtime hours. Your weekly salary was $800. Set up an equation that represents this.

40x + 12(2)(x)

40x + 24x

Writing Formulas

= 800

You work at a store making d dollars per hour. Last week, you worked 35 regular hours and h overtime hours, at time-and-a-half. Write a formula that expresses your weekly pay if you made $765.

Weekly Pay = 35d + hd(1.5)

= 35d + 1.5hd

Writing Formulas

= 765

When you are given the number of hours and weekly (or annually) salary, we can find the hourly rate by:

1. Writing an algebraic expression2. Doing any arithmetic that can be done3. Combine like terms4. Solve the equation (divide)

Solving for hourly rate

Last week, you worked a total of 52 hours, 40 of which were regular hours. You are paid x dollars per hour and are paid double time for all overtime hours. Your weekly salary was $800. Find your hourly rate

1. 40x + 12(2)(x) = 800

2. 40x + 24x = 800

3. 64x = 800→ x = 12.5

You made $12.50 per hour

Samantha worked her 40 regular hours last week, plus 7 overtime hours at the time-and-a-half rate. Her gross pay was $611.05. What was her hourly rate?

Let r = hourly rate

1. 40r + 7(1.5)(r) = 611.05

2. 40r + 10.5r = 611.05

3. 50.5r = 611.05 → r = 12.1

You made $12.10 per hour

Jillian worked her 40 regular hours last week, plus 2 overtime hours at a double-time rate. Her gross pay was $484. What was her hourly rate?

Let r = hourly rate

1. 40r + 2(2)(r) = 484

2. 40r + 4r = 484

3. 44r = 484 → r = 11

You made $11.00 per hour

Last week, Saul worked r regular hours and t

overtime hours at a time and-a-half rate. He earned $700. If x represents his hourly rate, express x in terms of r and h.

1. rx + t(x)(1.5) = 700

Solve for x

x (r + 1.5t) = 700→ x = tr 5.1

700

Last week, you worked a total of 55 hours, 40 of which were regular. For all overtime hours, you receive time-and-a-half. Your gross pay for the week was $643.75. Find your hourly rate.

1. 40r + 15(1.5)(r) = 643.75

2. 40r + 22.5r = 643.75

3. 62.5r = 643.75 → r = 10.3

You made $10.30 per hour

Steve worked 37 regular hours last week. His gross pay was $545.75. What was his hourly rate?

1. 37r + 0(1.5)(r) = 545.75

2. 37r + 0r = 545.75

3. 37r = 545.75

→ r = 14.75

You made $14.75 per hour

Krissy worked 40 regular hours last week, plus

8 overtime hours at the time-and-a-half rate. Her gross pay was $572. What was her

hourly rate?

1. 40r + 8(1.5)(r) = 572

2. 40r + 12r = 572

3. 52r = 572→ r = 11

You made $11 per hour

Mrs. Frasier worked her 40 regular hours last week, plus four overtime hours at the double-time rate. Her gross pay was $576. What was her hourly rate?

1. 40r + 4(2)(r) = 576

2. 40r + 8r = 576

3. 48r = 576→ r = 12

You made $12 per hour

Mr. Johnson worked 45 regular hours last week, and 8 hours of overtime at the time-and-a-half rate. What was his hourly rate if

his gross pay was $1,197?

1. 45r + 8(1.5)(r) = 1,197

2. 45r + 12r = 1,197

3. 57r = 1,197 → r = 21

You made $21 per hour

Liam worked 40 hours a week regular time and

8 hours a week overtime at the time-and-a-half rate. Last year, Liam earned a total of $41,912. What is his hourly rate?

→ Weekly Rate = $806

1. 40r + 8(1.5)(r) = 806

2. 40r + 12r = 806

3. 52r = 806→ r = 15.5

You made $15.50 per hour

Last week, Saul worked r regular hours and t overtime hours at the time-and-a-half rate. He earned $700. If x represents his hourly rate, express x in terms of r and h.

1. rx + tx(1.5) = 700

2. x(r + 1.5t) = 700

3. x = 1.5t r

700

Gary earns $42,990 per year. He is paid weekly. He currently has a $456-per-month car loan payment, and he pays $1,277 per

year for auto insurance. Is one week’s paycheck enough to pay his monthly auto loan and his monthly cost of insurance?

Weekly Pay = $826.73

Car Loan = $456

Insurance = $106.42

Total Bills: $562.42

He will make enough in one week to pay for his car with $264.31 left.