Reasoning with Equations
1. What is the difference between an expression and an equation?
2. Can you name 3 words that indicate each operation?
3. How do you evaluate an expression?
4. Explain how distribution can simplify a problem.
5. What are like terms?
6. How do you combine like terms?
7. What are inverse operations? Name them.
8. How do you solve equations?
9. What do you do when an equation has variables on both sides?
10. How do you transform equations? Why would you want to?
NJ Center for Teaching and Learning
~1~
www.njctl.org
Reasoning with Equations Chapter Problems
Vocabulary, Equations & Expressions
Classwork
1. Circle the constant and underline the coefficient for each expression below
a. 5x – 3
b. 2x + 7
c. 2 – 4x
d. x + 3
2. Create an algebraic expression with a coefficient of 7 and a constant of 4.
3. Create an algebraic expression with a coefficient of -1 and a constant of -12.
4. Create an equation that contains a coefficient of 6.
5. Create an equation that contains a coefficient of -13.
6. What is the difference between an algebraic expression and an equation?
7. Which are algebraic expressions?
5x – 2
8x
w
14 + 5x
2w – 6
4x – 8 = 9
Homework
8. Circle the constant and underline the coefficient for each expression below
a. 3x – 5
b. 2x - 1
c. 7 – 8x
d. x + 2
9. Create an algebraic expression with a coefficient of 17 and a constant of 3.
10. Create an algebraic expression with a coefficient of -1 and a constant of -1.
11. Create an equation that contains a coefficient of 4.
12. Create an equation that contains a constant of -12.
13. What is the difference between an algebraic expression and an equation?
14. Which are algebraic expressions?
17m
8 – 3z
NJ Center for Teaching and Learning
w
9w + 4 = 12
~2~
12 + 7t
6y + 4
www.njctl.org
Translating between Words & Expressions
Classwork
Translate the words into an algebraic expression.
15. 4 times x
16. The sum of x and 6
17. The product of 9 and y
18. w less than 8
19. 5 more than x
20. The difference of 6 and x
21. 9 times the product of x and 4
22. The product of 5 and y divided by 3
23. The quotient of 300 and the quantity of x times 2
24. x less than 32
25. The quotient of 35 and the quantity of x minus 7
26. The product of 7 and x minus the quantity of 4 less than y
27. The quantity of 9 more than x divided by the quantity of 12 less than y
Homework
Translate the words into an algebraic expression.
28. The product of 14 and x
29. The quotient of x and 5
30. The sum of 19 and w
31. w less than 8
32. 7 less than x
33. The difference of 16 and y
34. 9 times the quotient of x and 20
35. The product of 6 and x less 3
36. The quotient of 100 and the sum of x and 2
37. x less than 2
38. The product of 5 and the quantity of x less than 7
39. The product of 27 and y divided by the quantity of 4 more than y
40. The quantity of 6 less than x divided by the quantity of 2 more than y
NJ Center for Teaching and Learning
~3~
www.njctl.org
Tables & Expressions
Classwork
Complete the table.
41.
42.
43.
n
5
10
15
3n
n
3
5
7
n+7
n
80
100
120
140
n - 70
44.
n
0
1
8
16
n÷8
45.
n
20
18
16
14
4 less than n
n
20
18
16
14
2 more than n
46.
NJ Center for Teaching and Learning
~4~
www.njctl.org
47. Adult ticket prices are $3 more than child ticket prices. Determine the adult ticket price, given the child
ticket price.
Child Ticket Price
$5
$7
$10
$12
Adult Ticket Price
48. Write an expression that represents the adult price, if the child price is “x”
49. For NJASK testing, 25 students are placed in each classroom. Determine the number of classrooms
needed, given the number of students testing.
Number of Students Testing
250
325
400
520
Number of Classroom Needed
50. Write an expression that represents the number of classrooms needed, if the number of students
testing is “x”
51. Mary has ½ the amount of money that Jim has. Determine the amount of money that Mary has, given
Jim’s amount of money.
Jim’s amount of money
$50
$100
$175
$220
Mary’s amount of money
52. Write an expression that represents the amount of money Mary has, given the amount of Jim’s
money.
53. Each person running in the race paid $20. Determine the amount of money collected, given the
amount of people running in the race.
Number of People Running Amount of Money Collected
150
230
410
520
54. Write an expression that represents the amount of money collected, given the number of people
running in the race.
Write an expression for the following situations.
55. Bob weighs 7 more pounds than Jack. Jack weighs x pounds. Bob’s weight:
56. Tiffany has 6 dollars less than Jessica. Jessica has x dollars. Tiffany’s money:
57. Samantha has 12 more stickers than Mike. Mike has S stickers. Samantha’s sticker amount:
NJ Center for Teaching and Learning
~5~
www.njctl.org
58. The recipe calls for twice the amount of sugar than flour. There is F amount of flour in the recipe.
Amount of sugar:
59. Mark’s quiz grade is one more than twice Ted’s quiz grade. Ted’s quiz grade is x. Mark’s quiz grade:
60. Laura paid x dollars for her prom dress. Beth paid four dollars less than Laura. Beth’s prom gown
price:
61. David ran the 5k in x minutes. Harry ran the same race in five minutes less than double David’s time.
Harry’s time:
62. The beans grew K inches. The tomatoes grew 3 inches more than triple the height of the beans.
Tomato height:
Create a scenario for the following expressions:
63. x + 5
64. 2(x – 3)
Homework
Complete the table.
65.
n 5+n
5
10
15
66.
n
3
5
7
67.
n
7n
n
10
80
100
120
140
NJ Center for Teaching and Learning
~6~
www.njctl.org
68.
n n÷2
0
1
8
16
69.
n 34 less n
20
18
16
14
70.
n 5 less than n
20
18
16
14
71. Child ticket prices are $3 less than adult ticket prices. Determine the child ticket price, given the adult
ticket price.
Adult Ticket Price
$10
$15
$20
$25
Child Ticket Price
72. Write an expression that represents the child price, if the adult price is “x”
73. For bussing, 40 students are assigned to each bus. Determine the number of busses needed, given
the number of students riding.
Number of Students Riding
240
320
400
500
Number of Busses Needed
74. Write an expression that represents the number of busses needed, if the number of students riding is
“x”
NJ Center for Teaching and Learning
~7~
www.njctl.org
75. The farm always has four times the number of chicks as hens. Determine the number of chicks,
given the number of hens.
Number of hens
20
40
50
60
Number of chicks
76. Write an expression that represents the number of chicks, given the number of hens.
77. Each person running in the race will eat two hotdogs. Determine the number of hotdogs needed,
given the amount of people running in the race.
Number of People Running
150
230
410
520
Number of Hotdogs needed
78. Write an expression that represents the number of hotdogs needed, given the number of people
running in the race.
Write an expression for the following situations.
79. Bob weighs 17 pounds less than Jack. Jack weighs x pounds. Bob’s weight:
80. Tiffany has 50 dollars more than Jessica. Jessica has x dollars. Tiffany’s money:
81. Samantha has 12 times as many stickers than Mike. Mike has S stickers. Samantha’s sticker amount:
82. The recipe calls for triple the amount of sugar than flour. There is F amount of flour in the recipe.
Amount of sugar:
83. Mark’s quiz grade is six more than double Ted’s quiz grade. Ted’s quiz grade is x. Mark’s quiz grade:
84. Laura paid x dollars for her prom dress. Beth paid 16 dollars more than Laura.
Beth’s prom gown price:
85. David ran the 5k in x minutes. Harry ran the same race in half the time that David ran the race.
Harry’s time:
86. The beans grew K inches. The tomatoes grew triple the height of the beans less 2 inches. Tomato
height:
Create a scenario for the following expressions:
87. 2(x + 3)
88. x - 4
NJ Center for Teaching and Learning
~8~
www.njctl.org
Evaluating Expressions
Classwork
Evaluate the expression for the given value
(2n + 1)2 for n = 3
2(n + 1)2 for n = 4
2n + 22 for n = 3
4x + 3x for x = 5
3(x – 3) for x = 7
8(x + 5)(x – 2) for x = 4
3x2 for x = 2
5x + 45 for x = 6
4x
for x = 10
5
98. 4y + x for x = 2 and y = 3
99. x + 17 for x = 12 and y = ½
y
100.
6x + 8y for x = 9 and y = ¼
101.
x + (2x – 8) for x = 10
102.
5(3x) + 8y for x = 2 and y = 10
89.
90.
91.
92.
93.
94.
95.
96.
97.
Use the distance formula, D = rt, to find the distance traveled
103.
104.
105.
Rate: 40 mph; Time: 2 hrs
Rate: 60 mph; Time: 5 hrs
Rate: 34 mph; Time: ½ hr
Homework
Evaluate the expression for the given value
106.
107.
108.
109.
110.
111.
112.
113.
114.
115.
116.
117.
118.
119.
(2n + 1)2 for n = 1
2(n + 1)2 for n = 3
2n + 22 for n = 5
4x + 3x for x = 6
3(x – 3) for x = 3
8(x + 5)(x – 2) for x = 6
3x2 for x = 8
5x + 45 for x = 3
4x
for x = 15
5
4y + x for x = 12 and y = 13
x + 17 for x = 2 and y = ½
y
6x + 8y for x = 8 and y = ¾
x + (2x – 8) for x = 11
5(3x) + 8y for x = 12 and y = 5
NJ Center for Teaching and Learning
~9~
www.njctl.org
Use the distance formula, D = rt, to find the distance traveled
120.
121.
122.
Rate: 14 mph; Time: 2 hrs
Rate: 60 mph; Time: ¾ hrs
Rate: 40 mph; Time: ½ hr
Distributive Property
Classwork
Use the Distributive Property to rewrite the expressions without parentheses
123.
124.
125.
126.
127.
(x + 4)
8(x – 2)
6(x + 4)
-1(x – 4)
(x + 2)8
Homework
Use the Distributive Property to rewrite the expressions without parentheses
128.
5(x + 4)
129.
7(x – 12)
130.
3(x - 14)
131.
-1(x – 2)
132.
(x - 2)5
Like Terms
Classwork
Create a like term for the given term.
133.
4x
134.
13y
135.
15x2
136.
16xy
137.
x
Homework
Create a like term for the given term.
138.
6x
139.
Y
140.
10x2
141.
14xy
142.
-5x
Combining Like Terms
Classwork
Simplify the expression if possible.
143.
144.
7x + 8x
6x + 8y + 2x
NJ Center for Teaching and Learning
~ 10 ~
www.njctl.org
145.
146.
147.
148.
149.
150.
151.
152.
153.
154.
155.
156.
157.
15x2 + 5x2
5x +2(x + 8)
-10y + 4y
9(x + 5) + 7(x – 3)
8 + (x – 4)2
7y + 8x + 3y + 2x
x + 2x
x2 + 5x2
2x + 4x + 3
6y – 3y
9y + 4y – 2y + y
x + 5x + x + 12
8x – 3x + 2x + 15
Homework
Simplify the expression if possible.
158.
159.
160.
161.
162.
163.
164.
165.
166.
167.
168.
169.
170.
171.
172.
17x + 18x + 3
6x + 8y - 2x – y
15x2 + 5x2 + 2x
5x +2(x + 8) + 3
-10y + 4y – 5
9(x - 5) + 7(x + 3)
18 + (x – 4)2 – 4
7y + 8x + 3y + 2x + 9
x + 2x + x + 5x
6x2 + 5x2
12x + 14x + 3y
6y – 3y + 6xy + 4xy
9y + 4y – 2y + y + y2
x + 5x + x + 12 – 7x
8x – 3x + 2x + 15 – 7y
Inverse Operations
Classwork
173.
Name the inverse operation needed to solve for the variable.
a. x + 9 = 17
b. y – 8 = 5
c. m + 5 = 21
d.
w
 12
6
e. 9v = 108
NJ Center for Teaching and Learning
~ 11 ~
www.njctl.org
Homework
174.
Name the inverse operation needed to solve for the variable.
a. t – 18 = 54
b. 14x = 228
c. m + 19 = 51
d. 11b = 66
e.
m
2
4
One Step Equations
Classwork
Solve.
175.
176.
177.
178.
179.
180.
181.
182.
183.
n + 7 = 20
x + 9 = -8
a – 15 = 27
y – 21 = -15
50 + w = 92
-4 + m = 18
m
 16
8
30 = 12m
-5m = 25
1
t  12
6
184.
185.
186.
187.
-10c = -80
n – (-6)= 12
-82 + x = -20
188.
r
5
2
Homework
Solve.
189.
190.
191.
n + 9 = 13
-14 + b = 21
z – 18 = -14
NJ Center for Teaching and Learning
~ 12 ~
www.njctl.org
192.
193.
194.
-7 + g = -12
19 = 15 + y
b + (-4) = 13
195.
q
 33
3
196.
197.
-18x = -360
x – 11 = 4
198.
1
n  15
5
199.
200.
201.
-15c = -75
-8 + r = 27
19 + m = 3
202.
w
1
8
Two Step Equations
Classwork
Solve.
203.
7x – 2 = 26
204.
½ (m – 3) = 12
205.
-6h – 6 = 30
206.
5x + 20 = -20
207.
3 = -3y – 15
208.
-24 = 14y – 5
209.
7r – 5 = 10
210.
9 = 16y + 51
211.
13x + 6 = 6
212.
x
 11  5
4
Homework
213.
2m – 8 = -28
NJ Center for Teaching and Learning
~ 13 ~
www.njctl.org
214.
x
38
9
215.
12m + 20 = -40
216.
x
 5  21
3
217.
8r – 27 = -19
6
218.
k
 33
3
219.
15 = -4y – 9
220.
8w + 4 = -36
221.
4a – 15 = -23
222.
44 = 5x - 6
Multi-Step Equations
Classwork
Solve.
223.
8s – (8 + 6s) = 20
224.
34 = 2x + 8(x + 3)
225.
226.
227.
3
( x  9)  15
4
2
( m  8)  4
3
35 = 22x – 12x + 5
NJ Center for Teaching and Learning
~ 14 ~
www.njctl.org
228.
6(b + 8) = 54
229.
99 = 33x + 3(3x + 5)
230.
–t + (5t – 7) = -5
231.
21 – 3(2 – w) = -12
232.
9 = 8b – (2b – 3)
Homework
Solve.
233.
6(m + 4) – 2m = -8
234.
44 = 4(8 + h)
235.
3
(8t  4)  2
4
0
236.
1
(10 h  15)  h
5
237.
3(5 – t) – 4t = 18
238.
2(y - 5) = 16
239.
0.1(h + 20) = 3
240.
3z
45
8
241.
8.6 = 6j + 4j
242.
12z – (4z + 6) = 82
NJ Center for Teaching and Learning
~ 15 ~
www.njctl.org
Variables on Both Sides
Classwork
Solve.
243.
18 – 5t = t
244.
3m – 6 = 5m + 8
245.
22w – 42 = 34 – 16w
246.
r + 6 – 5r = 14 – 2r
247.
6x + 12 = 4x
248.
4n – 14 = -16n + 26
249.
y – 2y + 3 = 3 – y
250.
4u – 7 = u + 3(4 + u)
251.
4m – (8 – m) = 6 – 2m
252.
3b + 16 = 5b + 16 – 2b
Homework
Solve.
253.
2m = 24 + 3m
254.
5w – 17 = 12 – 5w
255.
2p – 9 = 5p + 12
256.
35 – y = 4y
257.
10x = 4x – 8x + 7
258.
2s + 16 = s – 25
259.
14 – (2c + 5) = -2c + 9
260.
20 – 16p = 4(5 – 4p)
261.
4n + 8 = 8 – 4n
262.
1.4h = 1.8h + 4.8 – 0.4h
NJ Center for Teaching and Learning
~ 16 ~
www.njctl.org
More Equations
Classwork
263.
264.
1
(6w  12)  6  2(w  2)
6
3
6(6 – 2a) = -27a (-4a + 6)
2
265.
2b + 4(b – 6) = -2(2b – 14) + 98
266.
4g + 3(g – 2) = -5(g – 4) – g
267.
-7 + 8(5 – 3s) = 3(7 – 9s)
268.
The sum of the ages of the three Romano brothers is 63. If their ages can be represented
as consecutive integers, what is the age of the middle brother?1
Homework
269.
2
(9 x  15)  17  3( x  12)
3
270.
2(3x – 4) = -2x + 40
271.
3(1 + 2x) – 4x = -(x + 30)
272.
8g + 6(g – 2) = -10(g – 4) – 2g
273.
12(3n – 7) + 8n = -2(4 – 3n)
274.
Arielle has a collection of grasshoppers and crickets. She has 61 insects in all. The number of
grasshoppers is twice the number of crickets. Find the number of each type of insect that she
has2.
Literal Equations
Classwork
275.
Solve for w. A = lw
276.
Solve for m.
277.
Solve for b.
1
t
vm
3
16c  10b  2
From the New York State Education Department. Office of Assessment Policy, Development and Administration. Internet.
Available from www.nysedregents.org/IntegratedAlgebra; accessed 17, June, 2011.
2
From the New York State Education Department. Office of Assessment Policy, Development and Administration. Internet.
Available from www.nysedregents.org/IntegratedAlgebra; accessed 17, June, 2011.
NJ Center for Teaching and Learning
~ 17 ~
www.njctl.org
278.
Solve for h.
279.
Solve for
A
1
bh
2
4
3
 . V   r3
Homework
280.
Solve for l. P = 2l + 2w
281.
Solve for c.
282.
Solve for s.
283.
Solve for h. V  2r h
284.
Solve for h.
bc
5
20 x  5s  8
2
A
285.
p
1
(b1  b2 )h
2
The formula for the volume of a right circular cylinder is V = πr2h.
The value of h can be expressed as3
a.
b.
c.
𝑉 2
𝑟
𝜋
𝑉
𝜋𝑟 2
𝜋𝑟 2
𝑉
d. 𝑉 − 𝜋𝑟 2
286.
If c = 2m + d, then m is equal to4
1.
2.
𝑐−𝑑
𝑐
2
2
−𝑑
3. 𝑐 −
𝑑
2
4. 𝑑 − 2
3
From the New York State Education Department. Office of Assessment Policy, Development and Administration. Internet.
Available from www.nysedregents.org/IntegratedAlgebra; accessed 17, June, 2011.
4
From the New York State Education Department. Office of Assessment Policy, Development and Administration. Internet.
Available from www.nysedregents.org/IntegratedAlgebra; accessed 17, June, 2011.
NJ Center for Teaching and Learning
~ 18 ~
www.njctl.org
Unit Review
Reasoning with Equations Multiple Choice Questions
1.
3x and -2x
a. Are Like Terms
b. Are Unlike Terms
2.
5a and 5b
a. Are Like Terms
b. Are Unlike Terms
3.
4y and 5xy
a. Are Like Terms
b. Are Unlike Terms
4.
x2y and xy2
a. Are Like Terms
b. Are Unlike Terms
5.
22 and 14
a. Are Like Terms
b. Are Unlike Terms
6.
xy and –xy
a. Are Like Terms
b. Are Unlike Terms
7.
Match the expression 3(-4 + 3) with an equivalent expression.
a. 4(3) + 4(3)
b. 3(-4) + 3(3)
c. 4(3) - 4(3)
d. 3(4) + 3(3)
8.
Which algebraic expression represents the number of days in w weeks?
a. w – 7
b. w/7
c. w + 7
d. 7w
NJ Center for Teaching and Learning
~ 19 ~
www.njctl.org
9.
Which algebraic expression represents the number of hours in m minutes?
a. m – 60
b. m/60
c. m + 60
d. 60m
10.
In the expression 3x + 5, the value of 3 best describes:
a. the constant
b. the operation
c. the variable
d. the coefficient
11.
In the expression 2x + 16, the value of 16 best describes:
a. the coefficient
b. the variable
c. the operation
d. the constant
12.
Evaluate the expression 2x, when x = 10
a. 20
b. 12
c. 210
d.
13.
1
5
What operation is being performed between the number and variable in the expression
20
?
x
a.
b.
c.
d.
14.
addition
division
subtraction
multiplication
A group of 15 parents buys tickets to a fundraiser show and receives a group discount of $2
off the regular ticket price p. Which expression represents the total cost of the tickets, in
dollars?
a. 15 • p + 2
b. 15 • (p - 2)
c. p - 15 • 2
d. p • (15 - 2)
NJ Center for Teaching and Learning
~ 20 ~
www.njctl.org
15.
A music store sells CDs for $15 and tapes for $3. Which expression could be used to find the
dollar total of the sales for an hour if the store sold 8 CDs and 5 tapes?
a. (8 + 15) • (5 + 3)
b. (8 •15) + (5 • 3)
c. (8 • 3) + (5 •15)
d. (15 ÷8) + (5 ÷ 3a)
16.
There were three times as many adults as students attending a school play. If the
attendance was 480, how many adults and how many students attended the play?
a. 360 students, 120 adults
b. 240 students, 240 adults
c. 120 students, 360 adults
d. 160 students, 320 adults
17.
Which of the following is not a variable expression?
a. 4n
b. n + m
c. n - 4
d. 4 + 3
18.
What is the value of the expression x + y when x = 15 and y = 21?
a. 6
b. 30
c. 36
d. 42
19.
Evaluate n 2 - m when m = 7 and n = 8.
a. 9
b. -9
c. 57

d. 71
20.
Claire has had her driver’s license for three years. Bill has had his license for “b” fewer years
than Claire. Which expression can be used to show the number of years Bill has had his
driver’s license?
a. 3 + b
b. b + 3
c. 3 - b
d. b < 3
NJ Center for Teaching and Learning
~ 21 ~
www.njctl.org
21.
Which situation is best modeled by the expression 25 – x?
a. George places “x” more video games on a shelf with 25 games
b. Sarah has driven “x” miles of a 25 mile trip
c. Ameilia paid $25 of an “x” dollar lunch she shared with Ariel
d. George has 25 boxes full of “x” baseball cards each
22.
Evaluate -3x + 5 when x = -2
a. 11
b. -1
c. 1
d. -11
23.
Nine decreased by the quantity eight times a number “x”.
a. 8x - 9
b. 9 – 8x
c. 9x - 8
d. 8 – 9x
24.
Four more than the quotient of 25 and y.
a.
25
4
y
b.
y
4
25
c.
d.
25+4
𝑦
𝑦
25−4
Reasoning with Equations Short Constructed Response
30.
A rectangle is 6 inches longer than it is wide. Write and simplify an expression for the perimeter
of the rectangle in terms of the width w.
NJ Center for Teaching and Learning
~ 22 ~
www.njctl.org
31. You and a friend worked in the school store last week. You worked 4 hours less than your friend.
Let h be the number of hours your friend worked. Write an expression in simplest form that
represents the total number of hours you both worked.
32. A trail mix contains peanuts, raisins, and M&Ms. In the mix, the amount of peanuts is three
times the amount of M&Ms; and the amount of raisins is two times the amount of M&Ms. Let m
represent the amount of M&Ms. Write and simplify an expression for the total number of pieces
of food in the trail mix.
33. Write an expression containing three terms that is in simplest form. One of the terms should be
constant.
34. Simplify: 5 – 2(3x – 4) + x
35. Shelly lives 500 miles away. Paul drove 65 mph for 4 hours. How many more miles will it take
for him to arrive at Shelly’s house?
36. Evaluate the expression

NJ Center for Teaching and Learning
5
(F – 32) when F = 41
9
~ 23 ~
www.njctl.org
Reasoning with Equations Extended Constructed Response
37. At the video arcade, Jenny buys 25 tokens. She uses two tokens for each game she plays.
Write an expression for the number of tokens Jenny has left after playing g games.
Find the number of tokens Jenny has left after playing 1, 4, 6, 10 and 12 games.
38. Bob wants to go to the movies with his friends. The movie theater charges $8 per ticket. Bob’s
friends reserve $48.00 worth of tickets in advance. How many people in total can attend the movie?
Identify the variable
Identify the constant
Write an equation which includes the number of people attending the movie, the price of each
ticket, and the total cost of the movie.
39. Write an expression that has four terms and simplifies to 16x + 5.
Identify the like terms
Identify the coefficients
Identify the constant terms
NJ Center for Teaching and Learning
~ 24 ~
www.njctl.org
40. Mary is 5 years older than Bob. When Bob is 65, 70, and 75 years of age, what will Mary’s age
be? Complete the chart with an expression containing a variable to explain your answer.
Bob
Mary
41. A cell phone company is offering 2 different monthly plans. Each plan charges a monthly fee plus
an additional cost per minute.
Plan A:
$ 40 fee plus $0.45 per minute
Plan B:
$70 fee plus $0.35 per minute
a)
Write an expression to represent the cost of Plan A
b)
Write an expression to represent the cost of Plan B
c)
Which plan would be least expensive for a total of 100 minutes?
42. Chad complained to his friend that he had five equations to solve for homework. Are all
of the homework problems equations? Justify your answer.
Math Homework
1. (11x-5f)3
NJ Center for Teaching and Learning
~ 25 ~
www.njctl.org
2. 3(2x + 7)
43. The clerk at the bank desk says there is an initial charge of $50.00 to open up a bank account at
the Sunny Farms Bank. He then explains that after, every account added on will cost an additional
$15.50 each. The Smith Family is thinking of opening an account for the family.
a) Write an equation that represents the cost to open accounts for the family members.
b) What is the greatest amount of family members that could open a bank account
without exceeding a fee of $500?
c) How much money would it cost if Mom Smith, Dad Smith, Sister Smith, and Brother
Smith want to open an account, and Mom Smith has a special discount coupon of 15%
off the final price?
44. The Rainbow Phone Service Company has a monthly fee of $100 and an additional charge of
$6.00 for every data one goes over a month. The Cellular Phone Service Company has a monthly fee
of $80 and an additional charge of $10.00 for every data one goes over. The Gomez family is
deciding which of these two phone providers to subscribe to5.
a) Write an equation that represents the cost of each phone company’s monthly fee.
Let p = cost.
b) For what number of data over will the total monthly fee for both companies be the
same?
c) The Gomez family’s daughter went over 6 data last month. Which phone service will
save the Gomez family the more if the daughter repeats this bad habit next month?
5
From the New York State Education Department. Office of Assessment Policy, Development and Administration. Internet.
Available from www.nysedregents.org/IntegratedAlgebra; accessed 17, June, 2011.
NJ Center for Teaching and Learning
~ 26 ~
www.njctl.org
NJ Center for Teaching and Learning
~ 27 ~
www.njctl.org