WRITE A LINEAR COST FUNCTION WITH FIXED VARIABLE COSTS WORD PROBLEM

Problem 1 :

Schroder has a job as a piano player in a local nightclub. His salary consists of $175 a week plus $1.50 for each paid admission. His paycheck last week was for $340. How many paid admissions did the club have last week?

Solution:

Let x be the number of paid admission that the club had last week.

Fixed salary = 175

Each paid admission = 1.50 x

Paycheck amount last week = 340

175 + 1.50x = 340

1.50x = 340 - 175

1.50x = 165

x = 165/1.50

x = 110

So, number of admission were 110.

Problem 2 :

The Fluffy Lump Cat Toy Company rents a warehouse facility. There is a fixed cost of $1200 a month for rent and a variable cost of $5 per box of toys that are stored. If the total cost for this month was $1315, how many boxes of toys are being stored?

Solution :

Fixed cost = 1200

Variable cost = 5 per box

Let x be the number of toys are being stored.

Total bill = 1315

1200 + 5x = 1315

5x = 1315 - 1200

5x = 115

x = 115/5

x = 23

So, the number of boxes of toys are being stored is 23.

Problem 3 :

Hartz Rental Car Company charges $19.95 per day plus $0.10 per mile to rent a compact car. Lee rented a car for two days and the total bill was $89.75. How many miles did she drive?

Solution :

Fixed charge = 19.95

Rent per mile = 0.10

Total bill = 89.75

Let x be the number of miles she drive.

19.95 + 0.10x = 89.75

0.10x = 89.75 - 19.95

0.10x = 69.8

x = 69.8/0.10

x = 698

So, he has drive 698 miles.

Problem 4 :

The Dot Com Company is an Internet Service Provider that charges $12.95 a month for 6 hours and $0.25 for each additional hour. Last month, Katrina’s Internet bill was $21.20. How many hours was Katrina on-line last month?

Solution :

Fixed charge = 12.95 for 6 hours

Charge for each additional hour = 0.25

Let x be the each additional hour after the 6th hour.

Her internet bill = 21.20

12.95 + 0.25 x = 21.20

0.25x = 21.20 - 12.95

0.25x = 8.25

x = 8.25/0.25

x = 33

Including the 6 hours = 33 + 6

= 39 hours

Last month she was in 39 hours on line.

Problem 5 :

Zip-Plus is a company that adds bar codes to US Mail. They charge $100 for the first 500 pieces of mail and $0.10 for each additional piece. If a company’s total bill for bar coding was $143.20, how many pieces of mail were bar coded?

Solution :

Charge for first 500 pieces = 100

For each additional piece, the charge is 0.10

Total bill = 143.20

Let x be the additional number of pieces.

100 + 0.10x = 143.20

0.10x = 143.20 - 100

0.10x = 43.20

x = 43.20/0.10

x = 432

So, number of additional pieces is 432.

Problem 6 :

A rookie baseball player had a clause in his contract that paid him $175,000 a year plus $200 per hit. If his salary last season was $199,000, how many hits did he receive last season?

Solution :

Fixed pay = 175000

Let x be the number of hits.

Amount paid per hit = 200

His salary for the last season = 199000

175000 + 200 x = 199000

200x = 199000 - 175000

200x = 24000

x = 24000/200

x = 120

So, number of hits in the last month is 120.

Problem 7 :

Mr. Yang’s ISP (Internet Service Provider) charges are $10 a month for 8 hours of service plus $0.50 an hour for each hour over the initial 8 hours. If his ISP bill last month was $18.50, how many hours did he spend on-line?

Solution :

Fixed charge = 10 (including 8 hours)

Let x be the number of hours spent in on line.

Cost for each additional hour = 0.50

10 + 0.50x = 18.50

0.50x = 18.50 - 10

0.50x = 8.50

x = 8.50/0.50

x = 17

Number of hours spent in online = 17 + 8

= 25 hours