Linear Inequalities in Context

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. An order of breadsticks costs $7 and a pizza costs $13. 

• 7x + 13y < 81

• 7x + 13y ≥ 81

• 7x + 13y ≤ 81

• 7x + 13y > 81

What is the inequality pictured?

• y ≥ -4/3x + 3

• y > -4/3x + 3

• y > 4/3x + 3

• y ≤ 4x + 3

Michael is raising money for his football league. Chocolate bars sell for $2.50 each, and chocolate mints sell for $3.50 each. If Michael wants to raise more than $150, write an inequality showing the number of chocolate bars, b, and the number of chocolate mints, m, he must sell.

• 2.50b + 3.50m > 150

• 2.50m + 3.50b > 150

• 2.50b + 3.50m <150

• 2.50m + 3.50b <150

Brian, a costume designer for the Bluepoint City Opera, is making costumes for the chorus members in an upcoming performance. While costuming this group of singers, Brian must keep costs below $1,300. Male costumes cost $6 to make and female costumes cost $20.
x = the number of male costumes
y = the number of female costumes

Select the inequality in standard form that describes this situation.

Anywhere Airlines aims to collect a minimum of $8,200 in baggage fees from passengers every day. Passengers are charged $31 for each regular suitcase and $40 for each overweight suitcase. x = the number of regular suitcases y = the number of overweight suitcases Select the inequality in standard form that describes this situation.

The dance committee hired a DJ for the fall dance. The DJ charges $125 per hour in addition to $55 for an assistant. The committee wants to keep the total cost under $600. Which inequality represents the maximum amount of hours the DJ will play at the dance?

• 125x + 55 ≤ 600

• 125x + 55 ≥ 600

• 125x + 55 > 600

• 125x + 55 < 600

A student is buying hot chips and sodas from the corner store. She can choose any combination of chips and sodas, and she does not want to spend more than $20. If hot chips cost $2.50 each and sodas costs $1.75 each, which inequality represents all possible combinations of x hot chips and y sodas?

• 2.5x + 1.75y ≥ 20

• 2.5x + 1.75y ≤ 20

• 2.5x + 1.75y < 20

• 1.75x + 2.5y ≥ 20

Maggie’s parents are booking a band and a DJ for a sweet 16, and wants to keep the cost of entertainment under $1,200. A band can play for part of the time at an hourly rate of $150, and a DJ can play for the remaining time at an hourly rate of $79. Write an inequality to describe the possible combinations of x band time and y DJ time?

• 150x + 79y < 1200

• 79x + 150y ≥ 1200

• 150x + 79y ≤ 1200

• 79x + 150y ≤ 1200

An Uber’s rates are $1.35 per mile plus an additional $2.50 base fee. You have a weekly budget represented by B(x). Which inequality can be used to represent the amount of money you can spend without going over your budget.

• B(x) ≤ 1.35x + 2.50

• B(x) ≥ 1.35x + 2.50

• B(x) < 1.35x + 2.50

• B(x) > 1.35x + 2.50

The vet told Casey that her dog should weigh at most 70 lbs. Her dog currently weighs 106 pounds.  Casey set a goal that he would lose 4 pounds per week. Which inequality represents the number of weeks it take for Casey's dog to reach 70 lbs?

• 106 - 4x ≤ 70

• 70 + 4x ≤ 106

• 4x - 106 ≥ 70

• 106 - 4x< 70