Q2 Illuminate Practice

Consider the linear inequality 2x + 3y ≤ 12 in the context of planning a school event with a limited budget. Can you explain how this inequality could represent the budget limitations?

• The inequality represents the budget limitations by allowing unlimited spending on all categories.

• The inequality represents the budget limitations by ensuring that the total spending on different categories does not exceed the budget.

• The inequality represents the budget limitations by not considering any spending at all.

• The inequality represents the budget limitations by only allowing spending on one category.

A business manufactures two products, Product A and Product B. Each unit of Product A brings in a profit of $5, while each unit of Product B brings in a profit of $8. If the company wants to earn at least $100 in profit, what is the linear inequality that represents this scenario, considering 'a' as the number of units for Product A and 'b' as the number of units for Product B?

• 5a - 8b ≤ 100

• 5a + 8b ≥ 100

• 5a + 8b ≤ 100

• 5a - 8b ≥ 100

A bakery sells two kinds of pastries, Pastry A and Pastry B. Each unit of Pastry A brings a profit of $4, while each unit of Pastry B brings a profit of $7. If the bakery wants to earn at least $150 from selling these pastries, what would be the linear inequality representing this situation, where 'a' is the number of units of Pastry A and 'b' is the number of units of Pastry B?

• 4a + 7b ≤ 150

• 4a + 7b ≥ 150

• 4a - 7b ≤ 150

• 4a - 7b ≥ 150

A school is organizing a trip with a total budget of $500. Each student's transportation cost is $3 and lunch cost is $5. Formulate a linear inequality that represents the total budget in terms of the number of students (s) attending the trip.

• 3s + 5s ≤ 500

• 3s + 5s ≥ 500

• 3s - 5s ≤ 500

• 3s - 5s ≥ 500

A company manufactures two types of products, Product C and Product D. Each unit of Product C yields a profit of $6, while each unit of Product D yields a profit of $9. If the company wants to earn a minimum profit of $200 by producing c units of Product C and d units of Product D, how can this scenario be represented as a linear inequality?

• 6c + 9d ≤ 200

• 6c + 9d ≥ 200

• 6c - 9d ≤ 200

• 6c - 9d ≥ 200

A restaurant prepares two dishes, dish E and dish F. Each unit of dish E brings a profit of $10, while each unit of dish F brings a profit of $15. If the restaurant wants to earn at least $300 in profit, what would be the linear inequality representing the profit from producing e units of dish E and f units of dish F?

• 10e + 15f ≤ 300

• 10e + 15f ≥ 300

• 10e - 15f ≤ 300

• 10e - 15f ≥ 300

A factory makes two products, X and Y. Each unit of X gives a profit of $7 and each unit of Y gives a profit of $10. If the factory wants to make at least $350 in profit, what is the linear inequality that represents the profit from producing x units of X and y units of Y?

• 7x + 10y ≤ 350

• 7x + 10y ≥ 350

• 7x - 10y ≤ 350

• 7x - 10y ≥ 350

A club has $600 to spend on a picnic. Each member's transportation costs $4 and food costs $6. What is the inequality that represents the total cost for m members?

• 4m + 6m ≤ 600

• 4m + 6m ≥ 600

• 4m - 6m ≤ 600

• 4m - 6m ≥ 600

Tags

CCSS.7.EE.B.4B

A school is planning a field trip with a total budget of $400. Each student's transportation cost is $2 and lunch cost is $6. Formulate a linear inequality that represents the total budget in terms of the number of students (s) attending the trip.

• 2s + 6s ≤ 400

• 2s + 6s ≥ 400

• 2s - 6s ≤ 400

• 2s - 6s ≥ 400

A company manufactures two types of products, Product E and Product F. Each unit of Product E yields a profit of $7, while each unit of Product F yields a profit of $11. If the company wants to earn a minimum profit of $250 by producing e units of Product E and f units of Product F, how can this scenario be represented as a linear inequality?

• 7e + 11f ≤ 250

• 7e + 11f ≥ 250

• 7e - 11f ≤ 250

• 7e - 11f ≥ 250