Algebra1 Name____________________Unit1Review Mod______Date__________ 1) Find the error in Brian’s work below. Describe his error. Then, solve the equation with the correct solution. Justify each step of your solution. Brian’s Work: Given equation: 4 5𝑥 − 12 − 7𝑥 = 5𝑥 Step 1: 20𝑥 − 48 − 7𝑥 = 5𝑥 Step 2: 27𝑥 − 48 = 5𝑥 Step 3: −48 = −22𝑥 Step 4: !!

!"= 𝑥

Step 5: 𝑥 = !!!"

2) Jane has $7.50 to spend in the candy store. She likes lollipops and gumballs. Each lollipop costs $2.75, and each gumball costs $0.50. Jane buys one lollipop. a) Write an equation that represents this situation. Identify your variable and what it represents. b) If Jane buys only one lollipop, then what is the greatest number of gumballs Jane can buy? Show your work. 3) Given the equation, what is the value of 𝑤? Show your work. 12 − 6 𝑤 − 3 = 3 −5 − 3𝑤 + 21 4) Solve the inequality for 𝑝. Show your work. 4 − !

!(𝑝 − 3) > 7

5) Tasty Yogurt Manufacturing Co. makes 10 cents per container of plain yogurt that it sells and 12 cents per container of vanilla yogurt. They want to make a monthly profit of at least $3200. This month, Tasty expects to sell at least 12,000 cups of plain yogurt (𝑝), but no more than 15,000 cups of vanilla yogurt (𝑣). Part A: Which of the following inequalities represents this situation? Select ALL that apply. A. 10𝑝 + 12𝑣 ≥ 3200 B. 0.10𝑝 + 0.12𝑣 ≥ 3200 C. 𝑝 ≥ 12,000 D. 𝑝 ≤ 12,000 E. 𝑣 ≤ 15,000 Part B: If Tasty sold exactly 15,000 cups of vanilla yogurt, how many cups of plain yogurt will the company need to sell to meet their profit goal of at least $3,200? Show your work.

Algebra1 Name____________________Unit1Review Mod______Date__________ 6) The formula for area of a trapezoid is 𝐴 = !

!ℎ 𝑏! + 𝑏! , where ℎ is the height and 𝑏! and 𝑏! are

the lengths of the two parallel sides. Based on the formula, which of the following formulas are true? Select THREE that apply. YOU MUST SHOW WORK! A. 𝑏! =

!!!− 𝑏! B. 𝑏! = 𝑏! −

!!!

C. 𝑏! =!!!− 𝑏!

D. ℎ = !!

!!!!! E. ℎ = !

!!!!!

!!!!

7) Bobby collected plastic drink bottles and cans that could be recycled to raise money for his school. A recycle depot paid him $0.05 per can and $0.10 per plastic bottle that he brought in. If he raised over $80, what is the minimum number of plastic bottles he collected if he only collected 480 cans? Show your work. 8) A taxi driver charges $10.00 to board his car and $4.00 for every mile driven (x) which is represented by the linear equation below.

𝑝𝑦 = 4𝑥 + 10 The variable 𝑝 represents how many people are in the taxi so that they may split the bill evenly. IF two people will be riding in the taxi, what would be the first step in solving the linear equation for the cost of one person? A. Subtracting 2 from both sides because the cost is being cut in half. B. Multiplying both sides by 2 because the cost is being cut in half. C. Dividing both sides by 2 because the cost is being cut in half. D. Dividing only the right side by 2 because the cost is the only thing being cut in half. NOW, if the two people are in the taxi for 12 miles, how much will each person pay the taxi driver? Explain. 9) A bus traveling from Philadelphia to Boston travels at an average speed of 55 miles per hour. The bus stops for 1 hour halfway between Philadelphia and Boston. a) Write an equation that can be used to find the time in hours, t, it will take for the bus to reach Boston, if the distance between Philadelphia and Boston is 310 miles. b) Solve your equation from part a. Show your work. How long will it take the bus to reach Boston?

Algebra1 Name____________________Unit1Review Mod______Date__________ 10) Bobby has a sister named Abbey. Bobby’s sister Abbey is 4 years older than !

! of Bobby’s

age. a) Write an expression that represents Abbey’s age, using b to represent Bobby’s age. b) How old is Bobby if Abbey is 7 years old? Show your work. 11) Jane set up a lemonade stand to sell lemonade. The total cost of making the lemonade was $1.50. She sold each cup of lemonade for $0.25. Write and solve an equation that can be used to find the total number of cups, x, Jane must sell to make a profit of $9.75. (**Hint: Profit = Total money made – Cost) 12) Solve and graph the solution set to the inequality 4𝑥 + 10 < 6 . 13) Meg converted $100 to francs, and she then converted the francs to pounds. In the end, she had 100𝑓𝑝 pounds, where 𝑓 is the number of francs per dollar, and 𝑝 is the number of pounds per franc. What does 𝑓𝑝 represent? A. The number of dollars per pound B. The number of francs per pound C. The number of pounds per dollar D. The number of pounds per franc 14) Solve for 𝑥, if the perimeter 𝑝, equals 26 in the triangle below.