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Algebra Chapter 3 Study Guide


Multiple Choice
Identify the choice that best completes the statement or answers the question.
 
 
Solve the equation.
 

 1. 
–49 = x – 50
a.
–1
b.
1
c.
–99
d.
99
 

 2. 
14 = t + 7
a.
11
b.
7
c.
3
d.
21
 

 3. 
d + 0.7 = 0.9
a.
0.2
b.
–1.6
c.
–0.2
d.
1.6
 

 4. 
mc004-1.jpg
a.
mc004-2.jpg
b.
–14
c.
40
d.
–40
 

 5. 
mc005-1.jpgx = 27
a.
65
b.
13
c.
81
d.
72
 

 6. 
mc006-1.jpgx + 5 = 8
a.
mc006-2.jpg
b.
mc006-3.jpg
c.
mc006-4.jpg
d.
mc006-5.jpg
 

 7. 
11 = –d + 15
a.
11
b.
–4
c.
4
d.
6
 

 8. 
37 – 18 + 8w = 67
a.
–6
b.
4
c.
7
d.
6
 

 9. 
3(y + 6) = 30
a.
5
b.
16
c.
4
d.
–16
 

 10. 
4.9x + 4.4 = 19.1
a.
4
b.
3
c.
4.8
d.
7.2
 

 11. 
mc011-1.jpg
a.
–8
b.
2
c.
–10
d.
–4
 

 12. 
mc012-1.jpg
a.
16
b.
0.16
c.
4
d.
2.3
 

 13. 
mc013-1.jpg
a.
28
b.
mc013-2.jpg
c.
mc013-3.jpg
d.
3
 

 14. 
mc014-1.jpg
a.
3
b.
0
c.
–9
d.
–10
 

 15. 
5x – 5 = 3x – 9
a.
–2
b.
1
c.
–1
d.
–3
 

 16. 
Steven wants to buy a $565 bicycle. Steven has no money saved, but will be able to deposit $30 into a savings account when he receives his paycheck each Friday. However, before Steven can buy the bike, he must give his sister $65 that he owes her. For how many weeks will Steven need to deposit money into his savings account before he can pay back his sister and buy the bike?
a.
25 weeks
b.
19 weeks
c.
22 weeks
d.
21 weeks
 

 17. 
Find the value of y.
mc017-1.jpg
a.
18
b.
1.8
c.
–9
d.
9
 

 18. 
John and 2 friends are going out for pizza for lunch. They split one pizza and 3 large drinks. The pizza cost $14.00. After using a $7.00 gift certificate, they spend a total of $12.10. Write an equation to model this situation, and find the cost of one large drink.
a.
3d + $14.00 – $7.00 = $12.10; $1.70
b.
2d + $14.00 – $7.00 = $12.10; $2.55
c.
3d – $14.00 + $7.00 = $12.10; $9.55
d.
3d + $14.00 – $7.00 = $12.10; $1.90
 

 19. 
Find the measure of mc019-1.jpg. (Hint: The sum of the measures of the angles in a triangle is mc019-2.jpg.)
mc019-3.jpg
a.
mc019-4.jpg
b.
mc019-5.jpg
c.
mc019-6.jpg
d.
8mc019-7.jpg
 

 20. 
Peter is reading a 193-page book. He has read three pages more than one fourth of the number of pages he hasn’t yet read.
a. How many pages has he not yet read?
b. Estimate how many days it will take Peter to finish the book if he reads about 8 pages per day.
a.
144; about 18 days
c.
152; about 19 days
b.
147; about 18 days
d.
141; about 18 days
 

 21. 
The sum of two consecutive integers is 59. Write an equation that models this situation and find the values of the two integers.
a.
mc021-1.jpg; mc021-2.jpg; mc021-3.jpg
b.
mc021-4.jpg; mc021-5.jpg; mc021-6.jpg
c.
mc021-7.jpg; mc021-8.jpg; mc021-9.jpg
d.
mc021-10.jpg; mc021-11.jpg; mc021-12.jpg
 

 22. 
Carlos and Maria drove a total of 258 miles in 5 hours. Carlos drove the first part of the trip and averaged 53 miles per hour. Maria drove the remainder of the trip and averaged 51 miles per hour. For approximately how many hours did Maria drive? Round your answer to the nearest tenth if necessary.
a.
3.5 hours
b.
2.5 hours
c.
1.8 hours
d.
1.5 hours
 

 23. 
At 9:00 on Saturday morning, two bicyclists heading in opposite directions pass each other on a bicycle path.The bicyclist heading north is riding 6 km/hour faster than the bicyclist heading south. At 10:15, they are 42.5 km apart. Find the two bicyclists’ rates.
a.
northbound bicyclist = 20 km/h; southbound bicyclist = 14 km/h
b.
northbound bicyclist = 23 km/h; southbound bicyclist = 17 km/h
c.
northbound bicyclist = 18 km/h; southbound bicyclist = 11 km/h
d.
northbound bicyclist = 20 km/h; southbound bicyclist = 13 km/h
 

 24. 
The formula for converting degrees Celsius (C) to degrees Fahrenheit (F) is mc024-1.jpg. Solve the formula for degrees Celsius (C). Then find the temperature in degrees Celsius (C) when the temperature in degrees Fahrenheit (F) is –4.
a.
–20° C
b.
–29° C
c.
–14° C
d.
–7° C
 

 25. 
Solve the equation for a.
mc025-1.jpg
a.
mc025-2.jpg
b.
mc025-3.jpg
c.
mc025-4.jpg
d.
mc025-5.jpg
 
 
Solve the equation for the given variable.
 

 26. 
mc026-1.jpg; w
a.
mc026-2.jpg
b.
mc026-3.jpg
c.
mc026-4.jpg
d.
mc026-5.jpg
 

 27. 
mc027-1.jpg; x
a.
mc027-2.jpg
b.
mc027-3.jpg
c.
mc027-4.jpg
d.
mc027-5.jpg
 

 28. 
Determine whether the following statement is sometimes, always, or never true.
If two sets of data have the same range and the same mean then they have the same mode.
a.
sometimes
b.
always
c.
never
 
 
Solve the equation. If there is no solution, write no solution.
 

 29. 
mc029-1.jpg
a.
x = 13
c.
x = –1
b.
x = 13 or x = –13
d.
no solution
 

 30. 
mc030-1.jpg
a.
n = 14 or n = –14
c.
no solution
b.
n = 26 or n = –30
d.
n = 14
 

 31. 
mc031-1.jpg
a.
no solution
c.
h = –7, h = 21
b.
h = 21
d.
h = 7, h = –21
 

 32. 
The ideal width of a safety belt strap for a certain automobile is 5 cm. An actual width can vary by at most 0.35 cm. Write an absolute value inequality for the range of acceptable widths.
a.
mc032-1.jpg
c.
mc032-3.jpg
b.
mc032-2.jpg
d.
mc032-4.jpg
 
 
Solve the proportion.
 

 33. 
mc033-1.jpg
a.
55
b.
2.2
c.
110
d.
1.8
 

 34. 
mc034-1.jpg
a.
32
b.
40
c.
64
d.
72
 

 35. 
A van travels 220 miles on 10 gallons of gas. Write and solve a proportion to find how many gallons the van needs to travel 550 miles.
a.
mc035-1.jpg; 31 gallons of gas
c.
mc035-3.jpg; 115 gallons of gas
b.
mc035-2.jpg; 121 gallons of gas
d.
mc035-4.jpg; 25 gallons of gas
 

 36. 
The cross products of a proportion are ____ equal.
a.
always
b.
sometimes
c.
never
 

 37. 
What percent of 20 is 18?
a.
11.1%
b.
9%
c.
90%
d.
49.5%
 

 38. 
What percent of 105 is 70?
a.
mc038-1.jpg
b.
mc038-2.jpg
c.
50%
d.
70%
 

 39. 
60% of 60 is what number?
a.
18
b.
4
c.
36
d.
9
 

 40. 
What is 6% of 117?
a.
5.97
b.
8.07
c.
7.02
d.
7.37
 

 41. 
30% of what number is 42?
a.
210
b.
105
c.
140
d.
14
 

 42. 
A golf club plans a trip to Hawaii, and 74 members are going. If this is 50% of the club’s members, how many members are in the club?
a.
148 members
b.
296 members
c.
37 members
d.
370 members
 
 
Write an equation and solve. Round the final answer to the nearest tenth, if necessary.
 

 43. 
What is 52% of 100?
a.
mc043-1.jpg; 59.2
c.
mc043-3.jpg; 1.9
b.
mc043-2.jpg; 0.5
d.
mc043-4.jpg; 52
 

 44. 
16 is what percent of 34?
a.
mc044-1.jpg; 47.1%
c.
mc044-3.jpg; 2.1%
b.
mc044-2.jpg; 40%
d.
mc044-4.jpg; 51.8%
 

 45. 
68 is 78% of what number?
a.
mc045-1.jpg; 53
c.
mc045-3.jpg; 59.3
b.
mc045-2.jpg; 87.2
d.
mc045-4.jpg; 90.7
 



 
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