Exam 115 chapter 2 practice
Disclaimer: The actual ixam is different
Solve.
1) During one year, the Cheung's real estate bill included $332 for county services. Of this
amount, $132 went to the highway department. What percent did the county highway
department receive? (Round answer to two decimal places.)
1)
2) What number is 2000% of 367
2)
3) What number is 8.5% of 10
3)
4) What percent of 53 is 671?
4)
5) During one year, the Schmidt's real estate bill included $277 for miscellaneous services.
Of this amount, 38% went to the library fund. How much money did the library receive?
5)
6) 109 is 48% of what number?
6)
7) What percent of 168 is 10.9?
7)
8) A tax-exempt school group received a bill of $236.47 for educational software. The bill
incorrectly included sales tax of 7%. How much should the school group pay?
8)
9) 570 is 11.1% of what number?
9)
10) To finance her community college education, Marguerite takes out a Stafford loan for
$2200. After a year, Marguerite decides to pay off the interest, which is 9% of $2200. How
much will she pay?
10)
11) What number is 110% of 369
11)
12) To finance her community college education, Marguerite takes out a Stafford loan for
$2300. After a year, Marguerite decides to pay off the interest, which is 9% of $2300. How
much will she pay? Include units in your answer.
12)
13) 17 is 0.75% of what number?
13)
14) 51 is 115% of what number?
14)
15) What is 88% of 217
15)
16) What percent of 59 is 511?
16)
17) What percent of 36 is 36?
17)
1
18) A tax-exempt school group received a bill of $261.08 for educational software. The bill
incorrectly included sales tax of 7%. How much should the school group pay? Include
units in your answer.
18)
19) 56.9 is what percent of 8?
19)
20) What number is 8.4% of 24
20)
Solve. Label any contradictions or identities.
21) 2x + 3 + 5x = 8x + 3 - x
21)
Solve.
22) 191 = 10x + 11
22)
Solve. Label any contradictions or identities.
23) 25m - 80 = 5(5m - 16)
23)
24) 8r + 5 = 29
24)
25) 5m - 7 = 9 + 9m
25)
Solve.
Solve. Label any contradictions or identities.
26) 7x + 6 = 7(x + 8) + 5
26)
27) (y - 7) - (y + 6) = 4y
27)
28) 7x - (3x - 1) = 2
28)
29) 1 (15x - 25) = 1 (20x - 12)
5
4
29)
30) p - 3p = 4
3
8
30)
Solve.
Solve. Label any contradictions or identities.
31) 8(x + 6) - 6x - 24 = 24 + 2x
31)
32) 15 x + 1 x = 6x + 1 + 13 x
14
14
7 14
32)
33) 2 (7x - 1 ) - 3 = 1
3
6
4 4
33)
Solve.
2
Solve. Label any contradictions or identities.
34) 2x - x = 2
5
3
34)
35) 41 = 5x - 9
35)
36) a - 1 = -3
4 4
36)
37) -4.2q = -22.4 - 1.4q
37)
38) -10.8q + 1.8 = -17.8 - 1.0q
38)
39) 11(x - 44) = 22
39)
40) -8t + 10 = 8 - 4t - 5t
40)
41) 3x + 2 + 2x = 6x + 2 - x
41)
42) -6y + 5 = -9 + 6y
42)
Solve.
Solve. Label any contradictions or identities.
43) -6t - 6 = 8 + 5t
43)
44) 0.4(5x + 15) = 2.2 - (x + 3)
44)
45) 3x + 3 + 2x = 6x + 2 - x
45)
46) (y - 6) - (y + 7) = 9y
46)
47) 5x + 3 + 3x = 9x + 2 - x
47)
Solve.
Solve. Label any contradictions or identities.
48) 20x + 81 = 4(5x + 22)
48)
49) 5(7x - 1) = 20
49)
50) -8 = z - 4.5
50)
51) 12x - 2x = -50
51)
Solve.
3
Solve. Label any contradictions or identities.
52) 2 (2x - 1 ) - 3 = 1
3
6
4 4
52)
Solve.
53) (y - 4) - (y + 5) = 6y
53)
Solve. Label any contradictions or identities.
54) -8y - 1 = 6 - 6y
54)
55) -1.8 = y + 9.4
55)
56) 18(x + 3) = 6(3x - 5) + 84
56)
57) p - 3p = 3
3
8
57)
58) 13 x + 1 x = 5x + 1 + 11 x
12
12
6 12
58)
Solve.
Solve. Label any contradictions or identities.
59) 110 = 16x + 6x
59)
Graph the inequality, and write the solution set using both set-builder notation and interval notation.
60) x ≤ -5
60)
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
61) x ≤ -2
61)
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
62) x > 3
62)
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
63) x ≥ -3
63)
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
64) x < 1
64)
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
4
Convert to percent notation.
65) 15
50
65)
66) 1
4
66)
67) 4.4
67)
68) 34
50
68)
69) 4
10
69)
70) 2
20
70)
71) 4
71)
Use an inequality and the five-step process to solve the problem.
72) A shopkeeper is making a triangular sign for his store front, but he must keep the sign
under 20 ft2 to adhere to zoning laws. If the base of the sign is 2 ft, what is the maximum
height of the triangular sign?
72)
73) Jim has gotten scores of 95 and 91 on his first two tests. What score must he get on his
third test to keep an average of 95 or greater?
73)
74) One side of a rectangle is 6 inches and the other side is x inches. What values of x will
make the perimeter at least 36?
74)
Use an inequality and solve. Write the answer in set builder or interval notation.
75) One side of a rectangle is 14 inches and the other side is x inches. What values of x will
make the perimeter at least 44?
75)
Use an inequality and the five-step process to solve the problem.
76) One side of a rectangle is 14 inches and the other side is x inches. Find the value of x if
the area must be at least 140 square inches.
76)
77) A car rental company has two rental rates. Rate 1 is $63 per day plus $.14 per mile. Rate
2 is $126 per day plus $.07 per mile. If you plan to rent for one week, how many miles
would you need to drive to pay less by taking Rate 2?
77)
78) A bag of marbles has twice as many blue marbles as green marbles, and the bag has at
least 36 marbles in it. At least how many green marbles does it have?
78)
5
79) DG's Plumbing and Heating charges $50 plus $75 per hour for emergency service. Bill
remembers being billed just over $200 for an emergency call. How long to the nearest
hour was the plumber at Bill's house?
79)
80) The area of a triangle must be at most 14 square inches, the base is 4 inches, and the
height is x inches. Find the possible values for x.
80)
81) The color guard is making new triangular flags that must have a base of 18 inches to fit
on their flagpoles. What is the maximum length of the triangular flags, if they want to
use a maximum of 252 in. 2 of cloth?
81)
82) The equation y = 0.003x + 0.50 can be used to determine the approximate profit, y in
dollars, of producing x items. How many items must be produced so the profit will be at
least $1024?
82)
83) Jon has 824 points in his math class. He must have 90% of the 1000 points possible by the
end of the term to receive credit for the class. What is the minimum number of
additional points he must earn by the end of the term to receive credit for the class?
83)
Solve using the addition and multiplication principles. Write the answer in set builder or interval notation.
84) 25n + 20 ≤ 5(4n + 2)
84)
Solve using the addition and multiplication principles.
85) -13x - 7 ≥ -12x - 18
85)
86) -11 + 4z + 5 ≥ 3z + 4
86)
87) -7y + 2 ≤ -8y - 4
87)
88) 0.6x + 10 + x > 2x + 14 - 0.5x
88)
89) 12n - 24 ≤ 4(2n - 11)
89)
90) 5y - 12 ≥ 4y - 18
90)
91) x + 12 ≤ 7
2
91)
92) -20r - 10 ≤ -5(3r + 11)
92)
93) 9 + 3x < 48
93)
94) 2 (2x - 1) < 6
3
94)
6
2 -2 <3
95) 5 5x 15
6
5 5
95)
96) 6 + 6y ≥ 72
96)
Solve using the addition and multiplication principles. Write the answer in set builder or interval notation.
97) 3 + 4y + 2 ≥ 3y + 1
97)
Solve the formula for the indicated letter.
98) d = rt for r
98)
99) I = Prt for r (simple interest)
99)
100) A = 1 h(b 1 + b 2 ) for b 1
2
100)
101) 1 + 1 = c for b
a b
101)
102) F = 9 C + 32 for C
5
102)
103) V = 1 Bh for B
3
103)
104) 1 + 1 = 1 for c
a b c
104)
105) A = P(1 + nr) for r
105)
106) x = w + y + z
9
106)
for y
Convert the percent notation in the sentence to decimal notation.
107) Dietary Guidelines of the U.S Department of Agriculture recommend that Americans
limit fat intake to no more than 35% of calories.
Source: http://www.health.gov/dietaryguidelines/dga2005/recommendations.htm
108) People who work at home at least once per week, accounted for 15 percent of total
employment.
Source: Bureau of Labor Statistics http://www.bls.gov/news.release/homey.nr0.htm
Solve using the five-step problem-solving process.
109) If -6 is added to a number and the sum is doubled, the result is -7 less than the number.
Find the number.
7
107)
108)
109)
110) The second angle of a triangle is 3 times as large as the first. The third angle is 75° more
than the first. Find the measure of the smallest angle.
110)
111) The second angle of a triangle is 4 times as large as the first. The third angle is 120° more
than the sum of the other two angles. Find the measure of the second angle.
111)
112) If the first and third of three consecutive odd integers are added, the result is 69 less than
five times the second integer. Find the third integer.
112)
113) Two angles of a triangle are 40° and 110°. What is the measure of the third angle?
113)
Solve and show steps.
114) The sum of two consecutive integers is -223. Find the larger integer. Show steps.
114)
Solve using the five-step problem-solving process.
115) Kevin invested money in a savings account at a rate of 5% simple interest. After one
year, he has $4620.00 in the account. How much did Kevin originally invest?
116) Eric paid $560.77, including 6% tax, for an LCD computer monitor. How much did the
computer monitor itself cost?
Solve and show steps.
117) The complement of an angle measures 54° less than the angle. Find the measure of the
angle. Show steps.
Solve using the five-step problem-solving process.
118) The houses on the north side of Perry Street are consecutive odd numbers. Tom and
Voula are next-door neighbors and the sum of their house numbers is 578. Find their
house numbers.
115)
116)
117)
118)
Solve and show steps.
119) The difference between two positive integers is 60. One integer is three times as great as
the other. Find the integers. Show steps.
119)
Solve using the five-step problem-solving process.
120) The supplement of an angle measures 32° more than twice its complement. Find the
measure of the angle.
120)
Solve the problem.
121) In a local election, 42,700 people voted. This was an increase of 12% over the last
election. How many people voted in the last election? Round to the nearest whole
person if necessary.
8
121)
122) The wavelength w, in meters per cycle, of a musical note is given by w = r , where r is
f
122)
the speed of the sound in meters per second and f is the frequency in cycles per second.
The speed of sound in air is 344 m/sec. What is the wavelength of a note whose
frequency in air is 29 cycles per second? Round to the nearest tenth of a meter per cycle.
123) The perimeter of a rectangle with length L and width W is given by the formula
P = 2L + 2W. Find the perimeter of a rectangle with length 4 meters and width 5 meters.
123)
124) Midtown Antiques collects 5% sales tax on all sales. If total sales including tax are $
1885.68, find the portion that is the tax. Round to the nearest cent if necessary.
124)
125) After receiving a discount of 7.5% on its bulk order of typewriter ribbons, John's Office
Supply pays $3885. What was the price of the order before the discount? Round to the
nearest dollar if necessary."
125)
126) After spending $3950 for tables and $2550 for chairs, a convention center manager finds
that 15% of his original budget remains. Find the amount that remains. Round to the
nearest dollar if necessary."
126)
127) At many colleges, the number of "full-time-equivalent" students f is given by
f = n , where n is the total number of credits for which students enroll in a given
15
127)
semester. Determine the number of full-time-equivalent students on a campus in which
students registered for a total of 22,590 credits.
128) Brand X copier advertises that its copiers run 10% longer between service calls than its
competitor. If Brand X copiers run 60,800 copies between service calls, how many copies
would the competitor run (to the nearest copy)?
128)
129) At the end of the day, a storekeeper had $1030 in the cash register, counting both the sale
of goods and the sales tax of 3%. Find the amount that is the tax. Round to the nearest
dollar if necessary.
129)
130) The volume of a sphere with radius r is given by the formula V = 4 πr3. Find the
3
130)
volume of a sphere with radius 4 meters. Use 3.14 for the value of π .
131) The area of a triangle with base b and height h is given by the formula A = 1 bh. Find
2
131)
the area of a triangle with base 6 meters and height 15 meters.
Solve using the multiplication principle.
25
132) -5x = 18
4
132)
9
133) -40.0 = -8.0c
133)
5
134) 3x =
6
4
134)
Solve using the multiplication principle. Graph and write set-builder notation or interval notation for the answer.
135) -7 ≥ b
135)
6
136) - k < 4
5
136)
Graph on a number line.
137) x ≤ 1
137)
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
138) x < -7
138)
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
139) -3 < x < 1
139)
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
140) -4 ≤ x ≤ 0
140)
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
Select the equivalent equation that could be the next step in finding a solution to the equation.
141) 7x = 9 + 4x
A) 7x - 4x = 9
B) 11x = 9
C) 7x = 9
D) 7 x = 9
4x
4
142) 7(x - 2) = 9
A) 7x - 14 = 9
141)
142)
B) 7(x - 2) - 9 = 0
C) 7(x - 2) + 9 = 0
10
D) 7x - 2 = 9
Describe the graph using set-builder notation and interval notation.
143)
143)
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
144)
144)
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
145)
145)
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
146)
146)
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
Determine whether the given number is a solution of the inequality.
147) x ≤ -15, 0.7
147)
148) x ≥ 4, -9
148)
149) x ≤ 2, -8.7
149)
150) x < -6, -11
150)
Convert to decimal notation.
151) 0.8%
151)
152) 478%
152)
153) 51.8%
153)
Solve using the addition principle.
154) z - 1 = 0
39
154)
155) x + 7 = 8
11 11
155)
156) x - 2 = 1
3 27
156)
Convert the decimal notation in the sentence to percent notation.
157) Property is assessed at 0.13 of market value.
11
157)
Answer Key
Testname: 115CH2P
1) 39.76%
2) 7340
3) 0.85
4) 1266.0%
5) $105.26
6) 227.08
7) 6.5%
8) $221.00
9) 5135.14
10) $198
11) 405.9
12) $207
13) 2266.67
14) 44.35
15) 190.96
16) 866.1%
17) 100%
18) $244.00
19) 711.3%
20) 2.02
21) all real numbers; identity
22) 18
23) all real numbers; identity
24) 3
25) - 4
26) no solution; contradiction
27) - 13
4
28) 1
4
29) -1
30) -96
31) all real numbers; identity
32) - 2
81
33) 5
21
34) 30
35) 10
36) -11
37) 8
38) 2
39) 46
40) - 2
41) all real numbers; identity
42) 7
6
12
Answer Key
Testname: 115CH2P
43) - 14
11
44) - 34
15
45) no solution; contradiction
46) - 13
9
47) no solution; contradiction
48) no solution; contradiction
49) 5
7
50) -3.5
51) -5
52) 5
6
53) - 3
2
54) - 7
2
55) -11.2
56) all real numbers; identity
57) -72
58) - 2
57
59) 5
60) {x|x ≤ -5}, (-∞, -5]
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
61) {x|x ≤ -2}, (-∞, -2]
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
62) {x|x > 3}, (3, ∞)
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
63) {x|x ≥ -3}, [-3, ∞)
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
64) {x|x < 1}, (-∞, 1)
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
65) 30%
66) 25%
67) 440%
68) 68%
13
Answer Key
Testname: 115CH2P
69) 40%
70) 10%
71) 400%
72) 20.0 ft
73) At least 99
74) x ≥ 12
75) x ≥ 8
76) x ≥ 10
77) more than 6300 miles
78) At least 12 green marbles
79) 2 hours
80) 0 < x ≤ 7
81) 28 in.
82) x ≥ 341,167
83) 76 points
84) {n n ≤ -2} or (-∞, -2]
85) {x x ≤ 11} or (-∞, 11]
86) {z z ≥ 10} or [10, ∞)
87) {y y ≤ -6} or (-∞, -6]
88) {x x > 40} or (40, ∞)
89) {n n ≤ -5} or (-∞, -5]
90) {y y ≥ -6} or [-6, ∞)
91) {x x ≤ -10} or (-∞, -10]
92) {r r ≥ 9} or [9, ∞)
93) {x x < 13} or (-∞, 13)
94) {x x < 5} or (-∞, 5)
95) x x < 4 or -∞, 4
15
15
96) {y y ≥ 11} or [11, ∞)
97) {y y ≥ -4} or [-4, ∞)
98) r = d
t
99) r = I
Pt
100) b 1 = 2A - hb 2
h
101) b =
a
ac - 1
102) C = 5 (F - 32)
9
103) B = 3V
h
104) c = ab
a +b
14
Answer Key
Testname: 115CH2P
105) r = A - P
Pn
106) y = 9x - w - z
107) 0.30
108) 0.15
109) 19
110) 21°
111) 24°
112) 25
113) 30°
114) -111
115) $4400.00
116) $529.03
117) 72°
118) 288, 290
119) 30 and 90
120) 32°
121) 38,125 people
122) 11.9 meters per cycle
123) 18 meters
124) $89.79
125) $4200
126) $1147
127) 1506
128) 55,273 copies
129) $30
130) 267.95 m3
131) 45 m2
132) 10
9
133) 5.0
134) 10
9
135) {b b ≤ -42}, (-∞, -42]
-45
-44
-43
-42
-41
-40
-39
-19
-18
-17
136) {k k > -20}, (-20, ∞)
-23
-22
-21
-20
137)
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
138)
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
15
Answer Key
Testname: 115CH2P
139)
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
140)
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
141) A
142) A
143) {x|x ≤ 3}, (-∞, 3]
144) {x|x > -2}, (-2, ∞)
145) {x|x ≥ -2}, [-2, ∞)
146) {x|x ≥ -3}, [-3, ∞)
147) No
148) No
149) Yes
150) Yes
151) 0.008
152) 4.78
153) 0.518
154) 1
39
155) 1
11
156) 19
27
157) 13%
16