Try This
c. A public television station set a goal of $350,000 in pledges during a certain
month. The total pledged was $525,000. What percent of the station's goal
was reached?
d. A bread recipe calls for J cup of rye flour. You only have J .rrp on hand. What
percent of your original amount of rye flour will remain after baking the bread?
Extra Help
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examples at the Prentice
HallWeb site.
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1-6 Exercises
A
1. Tony's Baby-Sitting Service charges $8.50 per
What is the cost of a 7-hour baby-sitting job?
,
job plus $6.75 per hour.
Renting a rug shampooer costs $5.25 per hour plus $4.25 for the
shampoo. Find the cost of shampooing a rug if the time required is
3.5 hours.
3. The Jalopy Car Rental charges $32 per day plus $0.23 per mile. Find the
cost of renting a car for a 3-day trip of 320 miles.
4.
A phone company charges 409 per long distance call plus 209 per minute.
Find the cost of an 18-minute long distance phone call.
from Earth to the moon is about 240,000 mi.That is about
0.005 the distance from Earth to Mars. Find the approximate distance
5. The distance
from Earth to Mars.
6. Jamie gave Laura $3 more than Laura already had. Now Laura has $19.
How much did Jamie give her?
7. The height of the Statue of Liberty is 93 m. This is abott 0.27 the height
of the Hancock Building in Chicago. What is the approximate height of
the Hancock Building?
-1.
I
ln a 50 mi/h wind, the statue's
crown sways 3 in. while the torch's
tip sways 5 in. How many inches
does the crown sway per meter of
height from the base of the
pedestal?
8. The area of the Red Sea is about 1.8% of. the area of the Mediterranean
Sea. The area of the Red Sea is about 453,000 km. Find the approximate
area of the Mediterranean Sea.
point of aluminum is 1220 degrees Fahrenheit. This is 1.96
times the melting point of lead. What is the melting point of lead?
10. The area of the Pacific Ocean is about 239,000,000 km2. This represents
46%" ofEarth's area. What is the approximate area of Earth?
11. The Olympic time for men's 500-m speed skating has been decreasing by
about 0.1 seconds per year since 1924, when the record was 44.0 seconds.
Predict what the time will be in 201-0.
L2. The Olympic time for women's 500-m speed skating has been decreasing
by about 0.2 seconds per year since 1920, when the record was 54 seconds.
Predict what the time will be in 2010.
13. The Olympic time for men's 400-m hurdles has been decreasing by about
0.09 seconds per year since 1930, when the record was 52 seconds. Predict
what the time will be in 2010.
9. The melting
93m
I
1
1,-6 Writing Equations 33
15.
16.
17.
18.
The number of physicians in the United States has been rising at the rate
of about 17,000 per year since 1980, when there were about 467,700
physicians. Predict how many physicians there will be in the year 20L0.
A person invested in stock selling for $2613 per share. The stock value is
now $22)per share. What percent of the original investment is the
current stock value?
In 1995 the average American ate 48.8 lb of chicken. This was 6.3 lb more
than the average in 1990. What was the percent of increase in chicken
consumption from 1990 to 1995?
Between 1970 and 1980, the population of Sierra Vista, Arizona, grew
from 6689 to25,968. By what percent did the population increase?
The price of a computer was cut in half. Then it was cut another $34. The
new price was $338. What was the original price?
B
19. On Monday, Ramon bought five Zip
disks. Two days later the price of the
disks was decreased by $1.50 per disk. Leticia bought ten disks at the sale
price and paid $22 more than Ramon paid for five disks. What was the
original price of a disk?
Kirra is two years older than Reggie. Reggie is six times as old as Delia. The
average of their ages is nine years and four months. How old is each of them?
A gallon of one brand of paint covers approximately ! of the total wall
area of a room. A gallon of a different brand will cover about j of the
total wall area. After the first gallon is used, what percent of the
remaining wall area will the second gallon cover?
Critical Thinking Write a problem that can be solved by using the
equationl:)x+tO.
Challenge
23. At 6:00 a.u., the Wong family left for a vacation trip and drove south at
an average speed of 40 mi/h. Their friends, the Heisers, left two hours
later and traveled the same route at an average speed of 55 mi/h. At what
time could the Heisers expect to overtake the Wongs?
24. The tens digit of a two-digit number is three greater than the ones digit.
The difference between twice the original number and half the number
obtained after reversing.the digits is 108. What is the original number?
Self-Test
On the Web
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for a self-test at the
Prentice HallWeb site.
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34
Chapter
1
,
MflEs<ed ffiew5ewr
-..
* 4c - 9c 27. x - 9x
:
30. 34t - 7 :70
Solve. 28.y+6:1.4 29.2/;x + 5 4
31. )r + 13:20
32. 6a + 18 : 54
33. -9w : 27
35. 9c + 4:31 + 18c 36. 4w+ 5 : 6ut + I
34. 5(n - 2) : -65
38.7c*15:1.6c-3 l-5
37.8-5y:11y-8
Collect like
terms.
25. L1,t
+
4t
26. 3c
1--3
1
Real Numbers, Algebra, and Problem Solving
f_
Extra Help
On the Web
2-2 Exercises
Look for worked-out
examples at the Prentice
Hall Web site.
A
Solve.
l.
2.
A12 cm piece of tubing is cut into two pieces. One piece is 4 cm longer
than the other. How long are the pieces?
A piece of rope 5 m long is cut into two pieces so that one piece is three
fifths as long as the other. Find the length of each piece.
www.phschool.com
, 3. The product of 6 and nine times a number is the same as the difference of
ten times the number andZ.What is the number?
consecutive odd integers such that the sum of the first, two
times the second, and three times the third is 82.
5. A pro shop in a bowling alley drops the price of bowling balls24o/o to a
sale price of $134.20. What was the original price?
6. An appliance store drops the price of a certain type of TV 18% to a sale
price of $410. What was the original price?
4. Find three
'
7. Money is borrowed at 11,7" simple
interest. After 1 year,$721.50 pays off
the loan. How much was borrowed originally?
8. Money is borrowed atl2o/o
simple interest. After 1 year, $896 pays off the
loan. How much was borrowed originally?
For Exercises 9 and 10, remember that the sum of the measures of a triangle is 180'.
'
'
,
9. The
second angle of a triangle is three times the first and the
less than twice the first. Find the measures of the angles.
third is 12"
10. The second angle of a triangle is four times the first and the third is 5'
more than twice the first. Find the measures of the angles.
For Exercises L1 and 12, remember that the area of a rectangle is / x a; (the
product of the length and the width), and the perimeter is2l + 2w.
L1. The perimeter of a college basketball court is 96 m and the length is 14 m
more than the width. What are the dimensions?
12. The perimeter of a certain soccer field is 310 m. The length is 65 m more
than the width. What are the dimensions?
13. A 20o/o raise in salary gives a new salary of $18,000. What was the old salary?
L4. A 7 .5o/o raise brings a salary to $46,225. What was the salary before the raise?
ffi.
Error Analysis The sentence "Given two
consecutive even integers, two times the first plus three times the second is
76." is ambiguous. Which of the following equations could NOT represent
See Exercise 5.
IEEIIEEII
the sentence?
A.. (2[zx + 3])(2x + 2)
C. 2(2x)(2x + 2) :76
L6. Write a Convincing
:76
8.2(2x) + 3(2x + 2):76
D.2(2x + 3[2x + 2)) :76
Argument
Write an argument to convince
a
classmate of your answer. to Exercise 15.
2-2
Using
Equations 69
,:H
17. The total cost for tuition plus room and board for one quarter at Southern
State University is $6584. Tuition costs $704 more than room and board.
What is the quarterly tuition fee?
'
L8. The cost of a private
pilot course is $4250. The flight portion costs $1500
more than the ground school portion. What is the cost of each?
B
19.
,
A student's scores on five tests are 93"/",89y",72o/r,B0o/o, and 96%. What
must the student score on the sixth test so that the average will be 88%?
20. The yearly changes in the population of a city for three consecutive years
are, respectiv ely, 20 o/o increase, 30 7o increas e, and 207" decrease. What is
the total percent change from the beginning to the end of the third year?
21. Three numbers are such that the second is the difference of three times
the first and 6 while the third is the sum of 2 and I the second. The sum of
the three numbers is 172. Find the largest number.
)', An appliance store
is having a sale on 13 VCR models. They are displayed
left to right in order of increasing price. The price of each VCR differs by
$60 from that of each adjacent VCR. For the price of the VCR at the
extreme righ!, a customer can buy both the second and the sixth models.
What is the price of the least expensive VCR?
,7 Multi-Step Problem A tank at a marine exhibit contains 2000
gallons of sea water. The sea water is 7.57o salt. How many gallons, to the
nearest gallon, of fresh water must be added to the tank so that the
mixtuie contains only 7Yo salt?
Is it sometimes, always, or never true that the sum of two consecutive odd
integers is an odd integer?
25. The perimeter of a square is 12 cm greater than that of another square. Its area
exceeds the area of the other by 39 cm2. Find the perimeter of each square.
26.
Critical Thinking Rewrite the problem of Example
solution the shorter piece of rope has a length of 16j feet.
1 so
that in the
Challenge
27. Diophantus spent one sixth of his life as a child, one twelfth as a young
man, and one seventh as a bachelor. Five years after he was married he
had a son who died 4 years before his father at half his father's final age.
How long did Diophantus live?
-F*lixed
ffieec**ffiJ
Collect like terms. 28. x2 + 3 +
(-2*') + 4
29.x4
+ xzy +
2xa
+ 2yx2 -
xy2
- 3a3b + 2ab2 - a2b 31.3x - lZx - 3 -?*-Dl
32.a2+b2+r,*(-o'-b2- c') -1
34, 3a2b2 - 9ab2 35. 30x2y + 6ry' - l2x3y 'l-l
Factor. 33.2x2 + 2x
30. a3b + 2a2b - 6ab2
1
Multiply. 36. (8.2 x
70
Chapter 2
Equations and Inequalities
10-3)(2 x
10')
t-e
=+F-
Try This
B
b. A painter can be paid in two ways.
Plan A: $500 plus $45 per hour
Plan B: $55 per hour
Suppose the job takes n hours. For what values of n is Plan A better for
the painter?
9.
Ina
75,9
2-5 Exercises
10.
11.
1
12.
Handymen are sometimes paid by
the job and sometimes by the hour.
See Try This b.
gffiqf Exffa HeIp
Y3.,J On theWib
Look for worked-out
examples at the Prentice
Hall Web site.
www.phschool.com
A car rents for $23.95 per day, plus $0.1-0 per mile. You are on a daily
budget of $76.00. Within what mileage must you stay to remain within
{
will be four tests. You have scores
of 89,92, and 95 on the first three. You must earn a total of 360 points to
get an A. What score on the last test will give you an A?
3. You are going to invest $25,000, part at 14o/o and part at 16%. What is the
most that can be invested at'1.4o/o to make at least $3600 interest per year?
4. You are going to invest $20,000, part at lZo/o and part at 16%. What is the
most that can be invested at 12o/o in order to make at least $3000 interest
pet year?
5. In planning for a school dance, you find that one band will play for $250,
plus 50% of the total ticket sales. Another band will play for a flat fee of
$550. In order for the first band to produce more profit for the school
than the other band, what is the highest price you can charge per ticket,
Multi-Step Problem
On your new job, you can be paid in one of
two ways.
Plan A: A salary of $500 per month plus a commission of 4o/" of total sales
Plan B: A salary of $750 per month plus a commission of 5o/o of total sales
over $8000
For what amount of total sales is Plan B better than Plan A, assuming
that total sales are always more than $8000?
7. Multi-Step Problem A chauffeur can be paid in two ways.
Plan A: $500.00 plus $9.00 per hour \
Plan B: $14.00 ppr hour
Suppose that the job takes n hours. For what values of n is Plan A better
for the chauffeur than Plan B?
8. Estimation A mason can be paid in two ways.
Plan A: $300.00 plus $24.40 per hour
Plan B: $38.80 per hour
Suppose that the job takes n hours. To the nearest 10 hours, estimate for
what values of n plan B is better for the mason than Plan A.
2
r
2. You are taking a history course. There
6.
Chapter
:
L3.
budget?
assuming 300 people attend?
80
.
Equations and Inequalities
l
Ch:
The
fired
Suptr
of
44
14.
r
L5. I
Aca
speci
16. I
17,. I
I
,*.
l
€
s
Solv'
21.
t
B
9. An investment of P dollars made at the simple interest rate r for / years
will grow to a total T : P * Prt. For an investment of $L0,000 to grow to
at least $12,000 in two years, what is the minimum interest rate at which it
can be invested?
In a science course, you must average 89 for an A. Your first three tests were
75,95, and 91.
10. If you have only one test remaining, what score do you need for an A?
1L. If you have two tests remaining, what do you need to average on the two
tests to receive an A?
12. After the first three tests, you find that you must average 90 or better on
your remaining tests for an A. How many tests do you have left?
tl. Critical Thinking Suppose that a machinist is manufacturing boxes
of various sizes with rectangular bases. The length of a base must exceed
the width by at least 3 cm, but the base perimeter cannot exceed 24 cm.
What widths are possible?
Challenge
: -L6t2 * urt * so tells the height at time t of a projectile
vertically
fired
from height so with initial velocity oo.
Suppose a projectile is fired vertically from ground level at an initial velocity
of 448 ft per second.
14. When will the projectile be higher than3072 ft?
The formula S
15. When, if ever, will the projectile's height exceed 10,000 ft?
A carpenter makes either a certain hourly rate of r dollars per hour, or a
special rate that is $5 per hour less if a fee of/ dollars is paid first.
16. For what number of hours is the hourly rate cheaper?
17. Next year the fee will be doubled, but the discount will be $7.50 per hour.
For what number of hours will the special rate be cheaper?
Efior
Anctlysis A student gave"2,4,6" as the answer to the problem
18.
"Find three consecutive even integers such that 10 times the largest value
exceeds the product of the other two by more than 40." Explain why the
student's answer iqnot entirely correct.
Reniew
Solve. 19. 2a * b = c,for a
21. ab * cd * ef : g,for c
: fi,rcr:-
20;
x
22.
A: 2rr *
2nrh,for
r
2-3
2-5
Using
Inequalities 81