The 1996 tax brackets for a single person are given in the following table.
Taxable Income 1 Tax T
1. 0 – 24,000 15% (I)
2. 24,000 – 58,150 28% (I – 24,000) +
3600
3. 58,150 – 121,300 31% (I – 58,150) +
13,162
4. 121,300 – 263,750 36% (I – 121,300) +
32,738.50
5. over 263,750 39.6% (I – 263,750) +
84,020.50
Source: 1040 Forms and Instructions, IRS, 1996
121)
Write the income range for line 5 as an inequality. Write the inequality that represents the
tax owed.
121)
Provide an appropriate response.
122)
An economics instructor told his class that the demand equation for a certain product is p=
400 –q2 and its supply equation is p= 20q+ 100. If the 400 –q2 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?
122)
123)
A company produces plastic parts for automobiles. The manufacturing process for one part
costs $28 per part for labor and material, plus $36,000 in fixed costs. Industry competition
dictates that they can charge no more than $42 for this part. How much should they reduce
the material and labor costs to satisfy a company policy of earning a profit after selling
2,000 units?
123)
124)
The sum of two real numbers is 12. The sum of their reciprocals is 1
3. Find the two
numbers.
124)
125)
Solve: 3(4x– 1) 2(x+ 4)
125)
126)
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?
126)
127)
Solve: x plus seven is a number 3 units from zero.
127)
128)
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?
128)
129)
Give the bounds of summation and the index of summation for
21
k=4
(13k + 2)
129)
130)
Express the sum in summation notation.
1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + … + 37
130)
18
131)
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?
131)
132)
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%
132)
133)
Solve: 2
3x– 1 = 4
133)
22
The 1996 tax brackets for a single person are given in the following table.
Taxable Income 1 Tax T
1. 0 – 24,000 15% (I)
2. 24,000 – 58,150 28% (I – 24,000) +
3600
3. 58,150 – 121,300 31% (I – 58,150) +
13,162
4. 121,300 – 263,750 36% (I – 121,300) +
32,738.50
5. over 263,750 39.6% (I – 263,750) +
84,020.50
Source: 1040 Forms and Instructions, IRS, 1996
134)
Write the income range for line 2 as an inequality. Write the inequality that represents the
tax owed.
134)
Provide an appropriate response.
135)
Solve: z– 2 2z– 3
2
135)
136)
Give the bounds of summation and the index of summation for
10
j=7
(j3–j2 + 6j– 1)
136)
137)
Solve: 3(x– 5) + 7 < 4(3 –x) + 7x– 20
137)
138)
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?
138)
The 1996 tax brackets for a single person are given in the following table.
Taxable Income 1 Tax T
1. 0 – 24,000 15% (I)
2. 24,000 – 58,150 28% (I – 24,000) +
3600
3. 58,150 – 121,300 31% (I – 58,150) +
13,162
4. 121,300 – 263,750 36% (I – 121,300) +
32,738.50
5. over 263,750 39.6% (I – 263,750) +
84,020.50
Source: 1040 Forms and Instructions, IRS, 1996
139)
Write the income range for line 3 as an inequality. Write the inequality that represents the
tax owed.
139)
Provide an appropriate response.
140)
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.
140)
141)
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?
141)
142)
Solve: 4 – 2x
–5>x+ 2
142)
143)
The sum of two integers is 21. The second integer is three more than twice the first integer.
Find both of the integers.
143)
144)
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?
144)
145)
Evaluate
13
k=10
(4k + 9)
145)
146)
Evaluate
44
i=1
(i2 + 4i)
146)
147)
A pet food company needs to calculate how much to charge for a bag of rabbit food that
costs $10 to produce. The fixed costs involved in production are $15,000. They want to start
making a profit after they have sold 4,000 bags of rabbit food. What is the least amount
they can charge to make this goal?
147)
Express the problem using absolute value notation.
148)
The absolute value of the difference of two numbers is equal to the absolute value of the
difference of the two numbers in reverse order.
148)
Provide an appropriate response.
149)
Evaluate
60
k=20
k
149)
150)
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?
150)
151)
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).
151)
152)
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.
152)
153)
Evaluate
60
k=1
k
153)
154)
Solve: x+ 1
–3< 5
154)
155)
Evaluate
55
i=1
(2i3+ 8i2– 6i + 7)
155)
25
156)
Simplify: |3 – 8| – |8 – 3|
156)
157)
Write without the absolute–value symbol: |1 –2|
157)
158)
An electronics company manufactures personal CD players which sell for $89. If the
production line has $81,000 in fixed costs and $44 per player in labor and materials, how
many must they sell to make a profit?
158)
Express the problem using absolute value notation.
159)
A number is always at least as large as the negative of its absolute value and at most as
large as its absolute value.
159)
The 1996 tax brackets for a single person are given in the following table.
Taxable Income 1 Tax T
1. 0 – 24,000 15% (I)
2. 24,000 – 58,150 28% (I – 24,000) +
3600
3. 58,150 – 121,300 31% (I – 58,150) +
13,162
4. 121,300 – 263,750 36% (I – 121,300) +
32,738.50
5. over 263,750 39.6% (I – 263,750) +
84,020.50
Source: 1040 Forms and Instructions, IRS, 1996
160)
Write the income range for line 1 as an inequality. Write the inequality that represents the
tax owed.
160)
Provide an appropriate response.
161)
Evaluate
5
i=1
13i
161)
162)
Three times x plus five is a number that is more than 4 units from zero. What are the
possible values for x?
162)
163)
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?
163)
164)
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?
164)
165)
Solve: |x| < 6
165)
166)
Car rental company A rents a compact car for $32 per day, while rental company B rents an
equivalent car for $21 per day plus an initial fee of $55. If a customer wants the cheaper
rate, when should he rent from company B?
166)
167)
A newspaper publisher finds that the cost of printing and distributing each copy of its
morning paper is $0.22. The revenue from subscribers is $0.20 per copy. The advertising
revenue is 12% of the revenue received from subscribers for all copies sold beyond 15,000.
Find the smallest number of copies which must be sold to break even.
167)
168)
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?
168)
169)
Evaluate
89
i=1
(8i + 5)
169)
170)
Evaluate
6
p=1
(6 –p)
170)
171)
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.
171)
172)
Suppose a company offers you a sales position with your choice of two methods of
determining your yearly salary. One method pays $15,000 plus a bonus of 3% of your
yearly sales. The other method pays a straight 13% commission of your sales. For what
yearly sales level is it better to choose the first method?
172)
173)
Solve: –2(x– 1) – 7 9x– (3 –x)
173)
174)
Solve: 5 – 2x> 3
174)
175)
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.
175)
176)
Simplify: |9–1|
176)
177)
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?
177)
Express the problem using absolute value notation.
178)
The absolute value of the quotient of two numbers is equal to the quotient of the absolute
values of the two numbers.
178)
Provide an appropriate response.
179)
Six minus four times x is a number that is at most 14 units from zero. What are the possible
values for x?
179)
180)
Evaluate
80
i=1
25
180)
181)
Solve: –x
3< 2
181)
182)
Solve: Two times x plus nine is a number 13 units from zero.
182)
183)
Evaluate
15
j=1
j3
183)
184)
Ten plus three times x is a number that is at most 11 units from 0. What are the possible
values for x?
184)
185)
Solve: 0.3 3 – 2x 4 1 – 0.3x
185)
186)
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?
186)
A zoo veterinarian can purchase 4 different animal foods with various nutrient values for the zoo’s grazing animals. Let
x1 represent the number of bags of food 1, x2 represent the number of bags of food 2, and so on. The number of bags of
each food needed can be described by the following:
x1= 150 –x4
0
x2= 3x4– 210
0
x3=x4+
60 0
187)
Develop an interval for each of the other variables.
187)
Provide an appropriate response.
188)
Solve: 5x– 2 14 – 3x
188)
189)
Solve: Three times x plus four is a number –4 units from zero.
189)
190)
What Celsius temperature C corresponds to a Fahrenheit temperature of F= 98.6 degrees
(normal body temperature) if F=9
5C+ 32?
190)
191)
Solve: a
2–a
3<a
5+ 1
191)
192)
Express the sum in summation notation.
4 + 6 + 8 + 10 + 12 + 14 + 16
192)
193)
The sum of a number and its square is 12. Find the number.
193)
194)
The owner of a floral shop wants to take out a loan to purchase a new delivery truck. The
company has current assets of $121,600 and current liabilities of $28,000. How much can he
borrow if he wants his current ratio of assets to liabilities to be no less than 2.8? (Note: The
funds they receive are considered as current assets and the loan as a current liability.)
194)
195)
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?
195)
196)
The cost of producing each copy of a travel guide is $0.95. It is sold to travel agents for
$0.90 each, and the amount received for advertising is 10% of the amount received for all
guides sold beyond 12,000. Find the fewest number of travel guides that must be sold to
break even.
196)
197)
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?
197)
198)
Evaluate
20
j=1
(j2 + 5j + 7)
198)
199)
The number x plus eight is at least 4 units from zero. What are the possible values for x?
199)
200)
Three minus three times x is a number that is more than 6 units from zero. What are the
possible values for x?
200)
201)
The number x minus four is less than 6 units from zero. What are the possible values for x?
201)
202)
Evaluate
112
i=21
(i3 + 4i2 + 7i + 10)
202)
203)
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?
203)
204)
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?
204)
205)
Three minus x is a number at least 6 units from zero. What are the possible values for x?
205)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the indicated sum.
206)
206)
A)
–14
B)
–5
C)
–35
D)
–30
Solve the problem.
207)
207)
A)
ak=6k +11; 10 weeks
B)
ak=6k +11; 9 weeks
C)
ak=6k +5; 9 weeks
D)
ak=6k +5; 10 weeks
Write the first five terms of the arithmetic sequence with the given first term a and common difference d.
208)
208)
A)
12, 9, 6, 3, 0
B)
9, 6, 3, 0, –3
C)
15, 12, 9, 6, 3
D)
12, 9, 5, 3, 0