Deck 2: Applications and More Algebra

Question 1

A company produces a product for which the variable cost per unit is $3.50 and fixed cost is $20,000 per year.Next year,the company wants the total cost to be $48,000.How many units of the product should be made next year?

Answer 1

8000

Question 2

Researchers at a university need a 10,000 square meter rectangular plot on which to grow three hybrids of corn.The plot is to be enclosed by fencing and divided into three equal subplots by a pair of fences both parallel to the same pair of sides of the rectangle.If 600 meters of fencing are to be used for the project,what are the dimensions of the plot?

Answer 2

50 m by 200 m,or 100 m by 100 m

Question 3

A good oiled furniture finish contains two parts boiled linseed oil and one part turpentine.If you need a pint (16 fluid ounces)of this furniture finish,how many fluid ounces of turpentine are needed?

A) 2
B) 3
C) 3
D) 4
E) 5

Answer 3

5

Question 4

The product of two consecutive integers is 42.Find the integers.

Question 5

A rectangular plot,4 meters by 8 meters,is to be used for a garden.The owner decides to put a pavement of uniform width inside the entire border so that 12 square meters of the plot is left for flowers.How wide should the pavement be?

Question 6

One of the most important defoliating insects is the gypsy moth caterpillar,which feeds on foliage of shade,forest,and fruit trees.A homeowner lives in an area in which the gypsy moth has become a problem.She wishes to spray the trees on her property before more defoliation occurs.She needs 128 ounces of a solution made up of 3 parts of insecticide A and 5 parts of insecticide B.The solution is then mixed with water.How many ounces of insecticide A should be used?

A) 16
B) 38.4
C) 48
D) 52
E) 68

Question 7

The sum of a number and its square is 12.Find the number.

Question 8

A company is establishing a dental plan for its employees.Under this plan the company will pay the first $20 of an employee's dental-care expenses and 80% of all additional dental-care expenses up to a maximum total benefit payment of $700.For an employee,find the total dental-care expenses covered by this program.

Question 9

A company manufactures two types of prefabricated houses: ranch and colonial.Last year they sold three times as many ranch models as they did colonial models.If a total of 2640 houses were sold last year,how many of each model were sold?

Question 10

A company manufactures hair dryers.The manufacturing cost is $9 per unit with a fixed cost of $16,000.A hair dryer sells for $15.If the company wants to earn a profit of $50,000,how many dryers must be sold?

Question 11

The IQ (intelligence quotient)of a person is found by dividing his or her mental age by his or her chronological age and then multiplying that result by 100.For example,a person with a a mental age of 11 and a chronological age of 10 has an IQ of
∙ 100 = 110.Find the mental age of a person with a chronological age of 12 and an IQ of 125.

Question 12

A person deposits $50 in a bank and in two years it increases to $56.18.If the bank compounds interest annually,what annual rate of interest does it pay?

Question 13

A certain machine can perform 34 chemical analyses per day,but a lab technician can perform only 7.Suppose a laboratory must make 110 analyses tomorrow and it has only two machines.How many technicians will be needed to complete the job?

Question 14

Approximately 21% of the air we breathe is oxygen.To the nearest milliliter,how many milliliters of air contain 1 milliliter of oxygen?

Question 15

An economics instructor told his class that the demand equation for a certain product is p = 400 -
and its supply equation is p = 20q + 100.If the 400 -
is set equal to the 20q + 100,then the positive solution to the resulting equation gives the "equilibrium quantity." The instructor asked his class to find this quantity.What answer should the class give?

Question 16

A sociologist is hired by a city to study different programs that aid the education of preschool-age children.The sociologist estimates that n years after the beginning of a particular program,p thousand preschoolers will be enrolled,where p =
n(12 - n).How many years after the start of the program will 25,000 preschoolers first be enrolled?

Question 17

The owner of a 20-room motel,which is 70% occupied,decides to charge $8 more than the single occupancy rate if two or more people occupy the room.This situation occurs in 75% of the occupied rooms,on the average.What should the two rates be so that the owner receives $160,000 in annual income to cover expenses and yield a reasonable profit? (Assume that a year has 365 days and give your answer to the nearest dollar.)

Question 18

The "current ratio" of a company is the value of its current assets divided by its current liabilities.A company has a current ratio of 2.5 and current liabilities of $80,000.what are its current assets?

Question 19

A theater owner charges $3 for each ticket.Currently,only 100 people attend the theater daily.The owner believes that for each $0.10 decrease per ticket,10 more people will attend.If this is true and the capacity of the theater is 200,what should the price of a ticket be if the owner wants to receive $375 daily from ticket sales?

Question 20

A company makes car stereos.The manufacturing cost for each stereo is $45.The company has fixed costs of $4150 per month.How many stereos can it make next month for a total cost of $10,000?

Question 21

A flower border of uniform width is to be added to a rectangular lawn,30 feet by 40 feet.How wide should the border be so that 600 sq ft of lawn remains?

Question 22

Suppose consumers purchase q units of a manufacturer's product when the price per unit (in dollars)is If no more than 75 units can be sold,then the number of units that must be sold in order that sales revenue be $1000 is

A) 20.
B) 25.
C) 40.
D) 50.
E) 75.

Question 23

An electric utility company is going to locate its new power plant along a straight road connecting the towns of Exton and Whyton,which are 10 miles apart.For political reasons,the utility company will buy coal from both towns.The price of coal per ton from Exton is $72.65 plus $0.45 per mile for delivery.The price per ton from Whyton is $72.25 plus $0.25 per mile for delivery.How far (in miles)from Exton should the plant be located if the price of coal per ton delivered from Exton is to be equal to that from Whyton? (Hint: If d is the distance of the plant from Exton,then 10 - d is the distance from Whyton.)

A) 2
B) 3
C) 3
D) 4
E) 6

Question 24

A chef must prepare 10 cups of a sauce.The recipe calls for 1 part wine and 4 parts beef stock.How much of each ingredient should be used?

Question 25

A group of biologists studied the nutritional effects on rats that were fed a diet containing 10% protein.The protein was made up of yeast and corn flour.By changing the percentage P (expressed as a decimal)of yeast in the protein mix,the group estimated that the average weight gain g (in grams)of a rat over a period of time was given by g = + 200P + 20.What percentage of yeast gave an average weight gain of 70 grams?

A) 50%
B) 60%
C) 65%
D) 70%
E) 80%

Question 26

A bank loaned $3320 to a company for the development of two products.If the loan for product A was $1520 more than the other,how much was loaned for each product?

Question 27

A baker must prepare 6 cups of pie filling.The recipe calls for
cup of sugar for each 4 cups of fruit.How much of each ingredient should be used?

Question 28

A metallurgist is preparing 63 kg of an alloy.It must consist of 3 parts aluminum and 4 parts copper.How much of each metal should be used?

Question 29

A rectangular field is twice as long as it is wide.Find the dimensions of the field if it needs 600 feet of fencing to go around the field.

Question 30

The sum of 3 integers is 27.The second is 3 more than the first,and the third is two more than twice the second integer.Find the three integers.

Question 31

An elder brother is twice as old as his younger brother at the present.Six years ago the elder brother was three times as old as the younger brother.Find the present age of the brothers.

Question 32

The sum of two real numbers is 12.The sum of their reciprocals is
.Find the two numbers.

Question 33

The sum of two integers is 21.The second integer is three more than twice the first integer.Find both of the integers.

Question 34

A chemist must prepare 540 ml of a chemical solution.It is to be made up of 4 parts acid and 5 parts distilled water.How much of each should be used?

Question 35

A homeowner needs to make a cover for a circular pool with a diameter of 18 feet.How much cover fabric should be ordered if the cover must extend 2 feet beyond the edge of the pool? (Hint: The area A of a circle is
,where r is the radius.Assume π = 3.14,and round to the nearest square foot.)

Question 36

A company will enclose a rectangular area of 12,800 square feet in the rear of its plant.One side will be bounded by the building and the other three sides by fencing.Suppose that 400 feet of fencing will be used and that the side of the building has a length of 100 ft.What will be the dimension (in feet)of the side of the rectangle that is opposite the building?

A) 20
B) 40
C) 60
D) 80
E) 90

Question 37

A rectangular deck attached to a ski lodge is 22 m long and 10 m wide.Planter boxes will be added along the 3 open sides,which include 1 long side and both short sides.How wide can the boxes be to leave 180 sq m of deck space?

Question 38

A company produces and sells q units of its product.If the variable cost is $4/unit,fixed costs are $4800 and the selling price is $28/unit,find the number of units the company must produce to split even (i.e.,zero profit).

Question 39

A person wishes to deposit a total fo $10,000 in two accounts.The savings account pays yearly interest of 4% and fixed certificates of deposit pay a yearly interest rate of 7%.How much should the person deposit in each account so that he gets a total of $502 interest at the end of the year?

Question 40

Imperial Educational Services (I.E.S.)wants to offer a workshop in pollution control to key personnel at Acme Corporation.I.E.S.will offer the course to thirty persons at a charge of $50 each.Moreover,I.E.S.will agree to reduce the charge for everybody by $1.00 for each person over the thirty who attends,up to a total group size of fifty.It has been determined that the greatest revenue the I.E.S.can receive is $1600.What group size will give this revenue?

A) 34
B) 36
C) 40
D) 44
E) 48

Question 41

Rooms in a 130 unit student housing complex are fully rented at $300 per month.The university is raising rates to produce $1920 more in monthly income from these units.Each $10 per month increase will create two vacancies with no possibility of filling them.What should be charged for the new rent?

Question 42

A woman has $90,000 to invest in two mutual funds.One fund is low-risk and has an annual yield of 10%.The second fund is medium-risk and has a 15% annual yield.How much should she invest in each fund if she would like to earn $10,000 per year from her investments?

Question 43

A company's revenue from the sale of interior doors is $98 per door.The cost of producing the doors is $48 per door with $12,000 in fixed costs.How many doors must the company sell in order to break even?

Question 44

A recliner costs a wholesaler $189 and her markup is 10% of her selling price.If the retailer's markup is 30% of his selling price for the item,what is the retailer's selling price?

Question 45

The owner of an 85 unit apartment building must raise the rent to cover an increase in property taxes of $9000 per year.At the current rent of $600 per month,each $30 per month increase will create one vacancy with no possibility of filling it.By how much should he raise the rent for these apartments?

Question 46

A homeowner will need $37,632 in 2 years to pay off a balloon mortgage on her house,but she has only saved $30,000 so far.At what annual interest rate,compounded annually,should she invest her savings in order to pay off her mortgage in 2 years?

Question 47

A computer keyboard retails for $48.54,which includes a markup of 40% for the retailer and a markup of 20% for the wholesaler.What did the keyboard cost the wholesaler?

Question 48

A corporation plans to buy back some of its stock in 2 years for $1,081,600.It plans to invest $1,000,000 this year to have the necessary capital for this move.At what annual rate of interest,compounded annually,should it invest this million dollars to earn enough for its stock re-purchase?

Question 49

A biotech company will require $10,112,400 to expand its research facility in 2 years.It has $9,000,000 to invest now for this purpose.At what annual rate of interest,compounded annually,should it invest this amount to be ready for construction in 2 years?

Question 50

An appliance company makes coffee makers for which the variable cost per unit is $12 and the fixed cost is $92,000.What should the selling price be for the company to earn a profit of $88,000 on 10,000 units?

Question 51

A painting contractor completed two jobs at $480 each.For one of them,this represented a 20% loss; for the other it was a 20% profit (based on his cost for each job).How much did he make or lose on the two jobs?

Question 52

A county decides to retire some of its road construction bonds in 2 years.At that time $4,840,000 will be required.If it presently sets aside $4,000,000,at what annual rate of interest,compounded annually,will this money need to earn in order for its future value to be sufficient to retire the bonds?

Question 53

A 100 unit high-rise apartment building which has no vacancy has come under new management.The new management company wants to receive $101,500 in monthly rent.They estimate that for each $50 per month increase over the current $950 per month rent,there will be three vacancies with no possibility of filling them.What rent should they charge for each apartment?

Question 54

A kitchen cabinet maker wants to establish a list price for a standard cabinet so that the selling price gives a trade discount of 10% of the list price.If he makes a markup of 20% of the selling price,and his cost is $144,what list price should he charge?

Question 55

A father wants to invest $50,000 in order to earn $4000 per year to help pay for his daughter's college education.He places $30,000 in a savings account earning 5% per year.He wants to place the rest of his investment in a mutual fund.How much will the mutual fund have to earn for him to make his goal?

Question 56

A car dealer has 20 new automobiles which she purchased for $12,000 each.If she sells 16 of them at a profit of 20%,for how much must she sell the remaining 4 to have an average profit of 18%?

Question 57

A teenager has $10,000 invested in a checking account paying 2.5% per year and a savings account paying 6.5% per year.The total interest earned in the two accounts at the end of the year was equivalent to an annual rate of 6% on the entire $10,000.How much was invested in each account?

Question 58

A fence is to be placed around a rectangular plot so that 2700 sq ft are enclosed.How much fencing must be used if the plot is 3 times as long as it is wide?

Question 59

A retired couple has $192,000 to invest.A safe investment yields 9.5% per year,but a riskier investment yields 12.5% per year.How much should they invest at each rate to earn $21,000 per year?

Question 60

A bicycle costs a wholesaler $63 and the wholesale selling price includes a markup of 25% of the wholesale selling price.What should be the retailer's selling price in order to make a profit of 30%

Question 61

Solve: 2(x - 8)+ 5 ≤ -4

Question 62

The solution of <
Is

A) x < -
B) x >
C) x <
D) x > 1
E) x< 1

Question 63

Solve: z - 2 ≥

Question 64

Solve: 0.2
< 0.8(x + 1)

Question 65

Solve:
+ 3 >

Question 66

The solution of 2(4 - 3x)≥ 10 + 4(x + 1)is

A) x ≥
B) x ≥ -
C) x ≤ -
D) x ≥
E) x ≥

Question 67

Solve: 3(4x - 1)≥ 2(x + 4)

Question 68

The solution of 5x >2x is

A) x > 0
B) x < 0
C) x <
D) x > -3
E) -∞ < x < ∞

Question 69

Solve: 7 - 2x < 9

Question 70

Solve:
≤ -

Question 71

The solution of 3x - 5 ≥ x - (4 - 2x)is

A) x ≥
B) x ≤ -
C) x ≥
D) no solution
E) -∞ < x < ∞

Question 72

The solution of 3 - 4(x + 5)< 3x + 7(4 - x)is

A) x < -
B) x >
C) x < 45
D) no solution
E) -∞ < x < ∞

Question 73

Solve: 5x - 2 ≥ 14 - 3x

Question 74

The solution of ≤ 2 - 7x is

A) x ≤ 1
B) x ≥ 1
C) x ≤
D) x ≥
E) ∅

Question 75

The solution of >
Is

A) x >
B) x <
C) x > -
D) x < -
E) x <

Question 76

The solution of -2(x - 3)< x is

A) -∞ < x < ∞
B) x < -2
C) x > -2
D) x > 2
E) x < 2

Question 77

Solve:
> x + 2

Question 78

Solve: -
≤ 9x - (3 - x)

Question 79

An office complex consists of 300 units which rent at $760 per month with no vacancies.Each $20 per month increase will create four vacancies with no possibility of filling them.The owner wishes to receive $233,600 per month from the complex.How much should the rent be increased to meet this goal?

Question 80

Solve: 4x - 3 < -2(1 - x)