Framing/Writing Linear Inequalities in Two Variables

Directions - For the scenario, identify the key components, then create an inequality to represent the situation. 

​To grow his ranch, a rancher is purchasing some bulls, which cost $3,200 apiece, and some cows, which cost $640 apiece. He doesn't want to spend more than $28,000 at this time.

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

​x = the number of bulls

​y = the number of cows

Which inequality written in standard form represents this scenario?

Justin charges $11 to mow a small lawn and $26 to mow a large lawn. He would like to make at least $130. Write an inequality that describes the situation. Let x = # of small lawns mowed and Let y = # of large lawns mowed

• 11x + 26y ≥ 130

• 11x + 26y > 130

• 11x + 26y ≤ 130

• 11x + 26y < 130

Harrison's crew team needs to raise at least $3,000 for their trip to the state championships. A sponsor generously donated hot dogs and cans of soda for the team to sell at each school sporting event. The crew team members will sell hot dogs for $2 each and soda for $1 each. What inequality can be used to calculate how many hot dogs, x, and sodas, y, Harrison's team needs to sell to have enough money for the trip?

• x + y ≥ 3000

• 2x + y ≤ 3000

• 2x - y ≥ 3000

• 2x + y ≥ 3000

In order to make some extra money, Justin is mowing lawns. He charges $11 to mow a small lawn and $26 to mow a large lawn. He would like to make at least $130. Write an inequality that describes the situation. Let x = # of small lawns mowed Let y = # of large lawns mowed

• 11x + 26y ≥ 130

• 11x + 26y ≤ 130

• 11x + 26y > 130

• 11x + 26y < 130

Sarah makes small purses (x) and big purses (y). She can make no more than 8 purses a week. It takes Sarah 2 hours to make small purses and 3 hours to make big purses. She has a maximum of 18 hours a week. Which inequality represents the amount of time available?

• 2x + 3y ≤ 18

• x + y ≤ 6

• x + y ≤ 9

• 3x + 2y > 18

Which of the following mathematical sentences illustrates a linear inequality in two variables?

• The value of twice a number x added by nine is less than 26.

• Thrice a number m is twice another number n.

• A number n multiplied by 8 results to twice a number p.

• Four times a number s subtracted from a number t is at most 33.

Write the linear inequality in standard form for this situation: Ms. Savva is ordering pizzas and breadsticks for a school party and has a budget of no more than RM81. An order of breadsticks costs RM7 and a pizza costs RM13.

• 7x + 13y < 81

• 7x + 13y ≤ 81

• 7x + 13y ≥ 81

• 7x + 13y > 81

The total ticket sales from a school play must be more than RM1500 to cover the expenses of producing the play. Student tickets are RM6 each and adult tickets are RM10 each. Write an inequality that represents how many adult and student tickets.

Write the linear inequality in standard form for this situation: Ms. Savva is ordering pizzas and breadsticks for a school party and has a budget of no more than 81.00. An order of breadsticks costs 7.00 and a pizza costs 13.00.

• 7x + 13y < 81

• 7x + 13y ≤ 81

• 7x + 13y ≥ 81

• 7x + 13y > 81

When creating a linear inequality, what is the third step?

• Find the total

• Identify the inequality for the total

• Identify the variables and the quantity associated (x = & y =)

• Write the inequality