7th Grade Math: Unit 2

Unit 2 – Item 1
Three students in math class are evaluating the expression below:

5(x - 4) + 2 + 4x

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Who is correct? Justify your thinking.

Unit 2 – Item 2
The annual cookie sale has begun at Rocky Road Middle School to raise funds for the seventh-grade end of the year activities. For all 268 students to attend a trip out of state, the grade level must raise at least $13,472. The school profits $14.00 for each container of cookie dough sold.

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Write an inequality using the given information to determine the number of containers, c, that the seventh-grade class needs to sale to attend the trip.

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How many containers must the seventh-grade class sell? Explain your reasoning.

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Unit 2 – Item 3
If Madison and Brenda both earn a wage of $11 per hour, and Madison was paid an additional $55 for overtime, which expression correctly represents Brenda's total pay separated from Madison's total pay?

Choose the correct expression and explain your reasoning.

A) 11(M+B) + 55
B) 11M + 55 + 11B
C) 11(M+B)
D) 11M + 11B + 55

Unit 2 – Item 4

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What is the perimeter of the figure above?

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What is the perimeter of the figure if a = 1/2 in.? Show your calculations step-by-step.

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Unit 2 – Item 5
Sarah is playing a number game. She thinks of a number, adds 5 to it, and then multiplies the result by 6. Surprisingly, her final answer is 66. What was Sarah’s original number? How do you know?

Unit 2 – Item 6
Designing a House Blueprint
You and your parents are having a new house built. As a resident of this house, you are being asked to help with drawing the blueprint so that the construction work can begin. Your parents ask for a house that has at least 3 bedrooms, 2 bathrooms, a kitchen, a dining room, and a living room. None of the rooms should have the same dimensions. The contractor stated that the acre of land only allows for a house that is 15x + 36 by 54x + 73. It is important that you include all the dimensions of the rooms as linear expressions in the blueprint.

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Construct a blueprint of the house for the contractors to follow. Each room must have its own dimensions. The opposite sides of each exterior wall should be equivalent

Unit 2 – Item 7
Emma is selling cookies to raise money for a school fundraiser. Each box of cookies she sells earns $3.50 for the fundraiser. Her goal is to raise at least $150 by the end of the week. So far, she has sold 15 boxes of cookies.

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Represent the scenario using an inequality and determine the number of boxes of cookies Emma needs to sell to reach her goal by the end of the week.

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Using the number line below, represent your solution from Part A.

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Unit 2 – Item 8
The Smith family is planning to rent a car for a day trip. The car rental company charges a flat fee of $80 plus $15 for each hour. They must pay for an entire hour, even if the car is returned early. For example, if they rent the car for 4 and a half hours, they must pay for a total of 5 hours.

If the Smith family wants to spend $150 or less on the car rental for the day, how many hours can they rent the car? Write and solve an inequality to determine the number of days the Smiths can rent the car and stay within budget.

Unit 2 – Item 9
The seventh-grade class is organizing a talent show as a fundraiser. They've decided to rent a banquet hall, which costs $700.

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If each ticket is priced at $15, how many tickets must they sell to achieve a minimum of $1000 in fundraising?

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How many tickets do they need to sell? Justify your answer.

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Unit 2 – Item 10
Emma works at a cafe where she earns $8.50 per hour plus an additional $120 in tips last week. She earned at least $395.50. If ℎ represents the minimum number of hours Emma could have worked, which inequality represents all the possible values of ℎ?

Unit 2 – Item 11
You are assuming the role of manager at a local grocery store responsible for ordering apples for the upcoming week.

Each bag of apples costs $10.50, and you have a budget of $200 allocated for purchasing apples. Additionally, you know that each bag contains 20 apples.

Your task is to determine the maximum number of bags of apples you can order while staying within your budget.

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PART A
Write an inequality to represent the situation. Solve the inequality to find the maximum number of bags of apples you can order within your budget.

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PART B
The price per bag of apples increases unexpectedly to $12.50 due to an increase in supplier costs. Adjust your inequality and find the new maximum number of bags of apples you can order within your budget.

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PART C
Based on findings in Part A and B, write a brief summary about the ordering of apples.

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Unit 2 – Item 12
Creating a Business Plan for Fresh Mart Grocery
You are part of a team of business analysts tasked with creating a comprehensive business plan for Fresh Mart Grocery, a local grocery store. Your goal is to assist the store owner in improving financial performance and achieving a monthly profit goal.

Business Data:

1. Monthly Income Sources:
Sales revenue from grocery items: $25,000
Additional income (e.g., service charges): $2,000
Total Monthly Income = $27,000
2. Monthly Expenses:
Rent: $5,000
Utilities (electricity, water, etc.): $1,500
Salaries (for all employees): $8,000
Inventory costs (purchase of goods): $7,000
Other operational expenses (cleaning, maintenance): $2,500
Total Monthly Expenses = $24,000
3. Financial Goal:
Monthly Profit Goal = $2,000
Student Directions
Write an inequality to represent the minimum sales revenue needed to achieve the profit goal.
Solve the inequality to determine the minimum sales revenue required for Fresh Mart Grocery.
Interpret the solution to understand the sales target necessary for profitability.
Prepare a business plan presentation including:
Overview of income sources, expenses, and profit goal.
Inequality representing minimum sales needed for profitability.
Solution to the inequality and interpretation of results.
Graphical representation of the inequality.
Recommendations or strategies to achieve the profit goal.

Who is correct? Justify your thinking.

Write an inequality using the given information to determine the number of containers, c, that the seventh-grade class needs to sale to attend the trip.

How many containers must the seventh-grade class sell? Explain your reasoning.

What is the perimeter of the figure above?

What is the perimeter of the figure if a = 1/2 in.? Show your calculations step-by-step.

Unit 2 – Item 5Sarah is playing a number game. She thinks of a number, adds 5 to it, and then multiplies the result by 6. Surprisingly, her final answer is 66. What was Sarah’s original number? How do you know?

Construct a blueprint of the house for the contractors to follow. Each room must have its own dimensions. The opposite sides of each exterior wall should be equivalent

Represent the scenario using an inequality and determine the number of boxes of cookies Emma needs to sell to reach her goal by the end of the week.

Using the number line below, represent your solution from Part A.

If each ticket is priced at $15, how many tickets must they sell to achieve a minimum of $1000 in fundraising?

How many tickets do they need to sell? Justify your answer.

Unit 2 – Item 10Emma works at a cafe where she earns $8.50 per hour plus an additional $120 in tips last week. She earned at least $395.50. If ℎ represents the minimum number of hours Emma could have worked, which inequality represents all the possible values of ℎ?

PART AWrite an inequality to represent the situation. Solve the inequality to find the maximum number of bags of apples you can order within your budget.

PART BThe price per bag of apples increases unexpectedly to $12.50 due to an increase in supplier costs. Adjust your inequality and find the new maximum number of bags of apples you can order within your budget.

PART CBased on findings in Part A and B, write a brief summary about the ordering of apples.

Unit 2 – Item 5
Sarah is playing a number game. She thinks of a number, adds 5 to it, and then multiplies the result by 6. Surprisingly, her final answer is 66. What was Sarah’s original number? How do you know?

Unit 2 – Item 10
Emma works at a cafe where she earns $8.50 per hour plus an additional $120 in tips last week. She earned at least $395.50. If ℎ represents the minimum number of hours Emma could have worked, which inequality represents all the possible values of ℎ?

PART A
Write an inequality to represent the situation. Solve the inequality to find the maximum number of bags of apples you can order within your budget.

PART B
The price per bag of apples increases unexpectedly to $12.50 due to an increase in supplier costs. Adjust your inequality and find the new maximum number of bags of apples you can order within your budget.

PART C
Based on findings in Part A and B, write a brief summary about the ordering of apples.