1. A store is advertising a sale with 10% off all items in the store. Sales tax is 5%.
(a) A 32-inch television is regularly priced at $295.00. What is the total price of the
television, including sales tax, if it was purchased on sale? Fill in the blank to complete the
sentence. Round your answer to the nearest cent.
The total cost of the television is $ ______.
(b) Adam and Brandi are customers discussing how the discount and tax will be calculated.
Here is Adam’s process for finding the total cost for any item in the store.
· Take 10% off the original price.
· Then, add the sales tax to the discounted price.
Adam represents his process as:
Here is Brandi’s process for finding the total cost for any item in the store.
· Determine the original price of the item, including sales tax.
· Then, take 10% off.
Brandi represents her process as:
In both equations, T represents the total cost of the television and p represents the regular
price.
Are they both correct? Use the properties of operations to justify your answer.
2. Look at the four diagrams below:
Which diagram does not result in the expression 4x + 4? Explain your answer fully.
3. When 6𝑥 − 2 is added to −9𝑥 + 6 the result is:
4.
If 𝑎 = 10𝑥 − 1 and 𝑏 = 𝑥 + 2, what is the value of 𝑎 + 𝑏?
5. Which two expressions are equivalent?
6. The numbers 5, 6 and 7 are an example of consecutive numbers, as one number comes
after another.
Another three consecutive numbers are added together so that the first number, plus two
times the second number, plus three times the third number gives the total.
Which of these expressions could represent the total? Check all that apply.
Explain your answer.
The total of the three consecutive numbers is 170. What are the numbers? Explain your
answer.
7.
8. Look at the four diagrams below:
Check every diagram that represents the expression 4x + 8:
Explain your answers.
9. Three consecutive numbers are added together and then their sum is multiplied by
three.
Some of the equations below represent the total using algebra. Check all that apply.
Explain your answers.
The total of the equation is 162. What are the three consecutive numbers? Explain your
answer.
10.
The sum of −9𝑥 + 7 and −4𝑥 + 4.
11.
When 8𝑥 + 6 is subtracted from −1𝑥 + 1 the result is:
12.
The result of subtracting −4𝑥 − 4 and −5𝑥 + 5.
13. If 𝑎 = −4𝑥7 and 𝑏 = 10𝑥 − 8, what is the value of 𝑎 − 𝑏?
14.
What is the factored form of 12𝑥 + 18?
15.
Expand 10(−10𝑥 + 8)?
16.
Kendrick Lamar says that 4(−1𝑥 + 5) − 1 and −9𝑥 − 37 are equivalent. Do you agree?
1
17. In a shipment of 1,000 bulbs, 40 of the bulbs were defective. What is the ratio of
defective to non-defective bulbs?
18. You are overseeing a project to install high speed rail between Washington DC and New
York City, a distance of 200 miles. After 3 months of work, your team has installed 60 miles
of track. When do you expect to finish the project?
19. You are flying from New York to San Francisco, a distance of 2,900 miles. After 4 hours
in flight, the pilot tells you that you have covered 2,100 miles. What is your unit rate in
miles per hour? When do you expect to arrive in San Francisco?
20. Two boys work at a job and agree to share the pay according to the number of hours
each works. One works 12 hours and the other 15 hours. The total pay for the job is 800
dollars. How much should each receive?
21. The Mount Major hike starts in Alton Bay, 716 feet above sea level. The summit is 1796
feet above sea level, and it takes about 45 minutes for a typical hiker to make the climb.
Find the rate at which this hiker gains altitude, in feet per minute.
22. Last week, Rihanna bought a DVD for $10.80 while the store was having a 25% off sale.
The sale is now over. How much would the same DVD cost today?
23. Drake owns a small bookstore in Cambridge, MA. Drake is ordering some copies of Flo
Rida’s latest book. Printer A sells the books at $350 per 100, and Printer B sells the books
at $150 per 40. Which company offers the lower price? Use the table below to compare
prices, give your answer and explain.
24. Miley Cyrus is running the Cincinnati Marathon. After 6 miles, Miley Cyrus’s clock reads
48 minutes. If Miley Cyrus maintains her currrent pace, what will her clock read at 20
miles? 26 miles? You can use the table below to calculate her times.
1.
Write each expression as the product of two factors.
a.
1∙3+7∙3
b.
(1 + 7) + (1 + 7) + (1 + 7)
c.
2 ∙ 1 + (1 + 7) + (7 ∙ 2)
d.
ℎ∙3+6∙3
e.
(ℎ + 6) + (ℎ + 6) + (ℎ + 6)
f.
2ℎ + (6 + ℎ) + 6 ∙ 2
g.
𝑗∙3+𝑘∙3
h.
(𝑗 + 𝑘) + (𝑗 + 𝑘) + (j + k)
i.
2𝑗 + (𝑘 + 𝑗) + 2𝑘
2.
Write each sum as a product of two factors.
a.
6∙7+3∙7
b.
(8 + 9) + (8 + 9) + (8 + 9)
c.
4 + (12 + 4) + (5 ∙ 4)
d.
2y ∙ 3 + 4 ∙ 3
e.
(x + 5) + (x + 5)
f.
3x + (2 + x) + 5 ∙ 2
g.
f∙6+g∙6
h.
(c + d) + (c + d) + (c + d) + (c + d)
i.
2r + r + s + 2s
3.
4.
Use the following rectangular array to answer the questions below.
a.
Fill in the missing information.
b.
Write the sum represented in the rectangular array.
c.
Use the missing information from part (a) to write the sum from part (b) as a product of two factors.
Write the sum as a product of two factors.
a.
81𝑤 + 48
b.
10 − 25𝑡
c.
12𝑎 + 16𝑏 + 8
5.
Xander goes to the movies with his family. Each family member buys a ticket and two boxes of popcorn. If
there are five members of his family, let 𝑡 represent the cost of a ticket and 𝑝 represent the cost of a box of
popcorn. Write two different expressions that represent the total amount his family spent. Explain how each
expression describes the situation in a different way.
6.
Write each expression in standard form.
7.
8.
a.
−3(1 − 8𝑚 − 2𝑛)
b.
5 − 7(−4𝑞 + 5)
c.
−(2ℎ − 9) − 4ℎ
d.
6(−5𝑟 − 4) − 2(𝑟 − 7𝑠 − 3)
Combine like terms to write each expression in standard form.
a.
(𝑟 − 𝑠) + (𝑠 − 𝑟)
b.
(−𝑟 + 𝑠) + (𝑠 − 𝑟)
c.
(−𝑟 − 𝑠) − (−𝑠 − 𝑟)
d.
(𝑟 − 𝑠) + (𝑠 − 𝑡) + (𝑡 − 𝑟)
e.
(𝑟 − 𝑠) − (𝑠 − 𝑡) − (𝑡 − 𝑟)
Rewrite the expressions by collecting like terms.
a.
c.
e.
1
2
3
𝑘− 𝑘
b.
8
1
1
3
1
2
5
3
2
4
2
3
6
− 𝑎− 𝑏− + 𝑏− 𝑏+ 𝑎
5
7
𝑦−
𝑦
14
d.
f.
2𝑟
5
+
7𝑟
15
3
1
5
10
−𝑝 + 𝑞 −
3𝑛
8
𝑛
𝑛
4
2
− +2
1
1
1
9
9
3
𝑞+ − 𝑝+2 𝑝
9.
Rewrite the expressions by using the distributive property and collecting like terms.
a.
d.
g.
j.
m.
p.
s.
4
5
(15𝑥 − 5)
b.
1
1
8
2
e.
8 −4( 𝑟 − 3 )
1
4
2
3
𝑘
2
3
(𝑝 + 4) + (𝑝 − 1)
5
3
1
3
4
3
4
(ℎ + ) − (ℎ + )
4𝑘
−
5
4
1+𝑓
5
−
−
1+𝑓
3
k.
n.
−3
3(5𝑔−1)
h.
2𝑔+7
6
+
3−𝑓
6
q.
4 1
( 𝑐 − 5)
c.
(14𝑥 + 7) − 5
f.
5 4
1
7
7
8
2
3
5
(𝑤 + 1) + (𝑤 − 3)
6
3
2
3
4
3
4
(ℎ + ) − (ℎ − )
3𝑡+2
7
−
+
3𝑑+1
5
𝑡−4
l.
o.
14
+
i.
𝑑−5
2
+
7
10
r.
4
2
1
5
3
6
2 𝑣 − (4𝑣 + 1 )
1
5
4
5
2
3
(5𝑥 − 15) − 2𝑥
1
(𝑐 − 1) − (2𝑐 + 1)
8
3
2
3
4
3
4
(ℎ + ) + (ℎ − )
9𝑥−4
10
9𝑤
6
+
+
3𝑥+2
5
2𝑤−7
3
−
𝑤−5
4