Download Chapter 2 Study Guide - St. Michael Catholic School

Middle Level Heading __________________________
Chapter 2 Study Guide
Solve each equation. Check your answer. If the equation is an identity, write identity. If it has
no real-number solution, write no solution.
1.
3n + 2 = –2n – 8
5n + 2 = -8
5n = -10
2.
1
3
z2
4
4
z+2=3
z=1
3.
x4 5

6
4
x – 4 = 30/4
x = 11.5
n = -2
4. 8x – 12 = 4x + 24
4x – 12 = 24
4x = 36
x=9
6.

1
(d 12)  4
4
5.
(3z + 4) = 6z 3(3z + 2)
-3z – 4 = 6z – 9z - 6
-3z – 4 = -3z - 6
– 4 = -6
no solution
7.–5(5.25 + 3.1x) = –6.2(2.5x + 1.9)
1/4d – 3 = 4
-26.25 + (-15.5x) = -15.5x + -11.78
1/4d = 7
-26.25 = -11.78
d = 28
no solution

Solve each equation. Justify your steps.
8.
8 + 3m = –7
3m = -15
m = -5
9.
Subtraction Property of Equality
Division Property of Equality

1
y 5 8
2
1/2y = 3
Subtraction Prop of Equality
y=6
Multiplication Prop of Equality
10. A youth club is taking a field trip to a community farm. 27 members attended the trip. The total
cost for the trip was $148.50. Write and solve an equation to determine the cost for each person.
Equation $148.50 = 27x
Solution $5.50 per person
Solve each equation for the given variable.
11. –3ab – 2bc = 12; c
12.
c f
 2
d g
-2bc = 12 + 3ab
12  3ab
c
2b
c
f
2 
d
g

c  d(

f
 2)
g
Define a variable and write an equation for each situation. Then solve.

13. A large cheese pizza costs $7.50. Each additional topping for the pizza costs $1.35. If the total bill for
the pizza Sally ordered was $12.90, how many toppings did she order?
Define variable: x = number of toppings
Solution: 4 toppings
Equation: $12.90 = $7.50 + $1.35x
14. A water park offers a season pass for $64 per person, which includes free admission and free parking.
Admission for the water park is $14.50 per person. Parking is normally $5 for those without a season
pass.
a. How many visits to the water park would you have to use for the season
pass to be a better deal?
Define variable: x = visits that make both deals equal
Equation: 64 = 14.50x + 5x
X = 3.28…
Solution: You would have to visit the park 4 times to make the season pass a better deal.
b. What would the total cost be for 3 visits with and without a season pass?
With the season pass, the cost is $64. Without the season pass, the cost is $58.50.
Convert the given amount to the given unit.
15. 60 ft; in
16. 3 mi; ft
17. 150 sec; min
720 inches
15,840 feet
2.5 minutes
18. A car went 25 miles per hour. What was the car’s average speed in feet per second?
25mi
1hr
5280 ft 132000 ft 36.6 ft




1hr
3600sec
1mi
3600sec
1sec
5 3

5
19. y
20.
-3y = 25
15z = 72
15 8

9 z


y=-25/3
y = 8
z = 72/15
1
3
10 z  8

4
16

21.

16(10) = 4(z-8)
160 = 4z – 32
4
z=
12
4
4
15
5
4d 1 3

d  9 2

22.

-2(4d+1) = -3(d+9)
-8d + (-2) = -3d + (-27)
192 = 4z
-5d + (-2) = -27
48 = z
-5d = -25
d=5
The figures are similar. Find the missing length. Round your answer to the nearest tenth.
23. m = _____________
10 7

m 18

m = 25.7
24. You project a drawing 7 inches wide and 4
1
inches tall onto a wall. The projected image is 27
2
inches tall. How wide is the projected image?
7 4.5

x 27


x = 42 inches
25. What percent of 37 is 111?
26. What is 72% of 150?
111 = 37x
3=x
x = 0.72(150)
x = 108
27. 60% of what number is 102?
0.6(x) = 102
x = 170
300%
Tell whether each percent change is an increase or decrease. Then find the percent
change. Round to the nearest tenth of a percent.

28. Original amount: $27
New amount: $30
increase
29. Original amount: $250
New amount: $200
Decrease
30  27 3

 0.1  11.1%
27
27
30. Original amount: 873
New amount: 781
decrease
250  200 50

 0.2  20%
250
250
31. Original amount: 4.7
New amount: 6.2
increase

873  781 92

 0.105...  10.5%
873
873

6.2  4.7 1.5

 0.241...  31.9%
4.7
4.7



32. The scale on a map is 1 in : 25 mi. You measure 6.5 in. between two towns. What is the actual
distance?
1in
6.5in

 6.5(25)  1x  162.5miles
25mi
x
33. In 1970, the U.S. population was about 205 million people. In 2007, it was about 301 million. What
was the percent increase? Round your answer to the nearest tenth of a percent.
301  205 96

 0.468...  46.8%
205
205
Find the percent error in the estimation. Round to the nearest percent.
34. You estimate that a tree is 45 feet tall. It is actually 58 feet tall.
45  58 13

 0.224...  22.4%
58
58
35. Write a problem that can be solved using similar polygons. Draw a diagram and solve the problem.


36. Write a multi-step equation for each condition listed below.
a. equation has no solution
b. equation has one solution
c. equation is an identity
37. The average class grade went from 79% to 85%. Your friend thinks this represents a 6% change in
the average. Explain your friend’s error. What is the actual percent increase rounded to the nearest tenth
percent?
85  79 6

 0.075...  7.5%
79
79
The friend subtracted 79% from 85% to get 6%. The actual percent increase is calculated above to be
7.5%.