Framing/Writing Linear Inequalities in Two Variables

Kim is using two mobile networks. Network one charges RM0.30 for every minute of call and network two charges RM0.38 for every minute of call. Kim spends at least RM68 monthly for calls. Which of the following inequalities is best to represent Kim's situation?

• 0.30x + 0.38y < 68

• 0.30x + 0.38y > 68

• 0.30x + 0.38y ≤ 68

• 0.30x + 0.38y ≥ 68

A fast food restaurant charges $6 for chicken nuggets and $3 for fries. You are buying lunch for yourself and your friends, but you only have $30.

x: number of chicken nuggets

y: number of fries

Which inequality represents the constraints.

Alvin, a mechanic, earns $17 for every oil change, x, he performs and $77 for every tune-up, y. He needs to earn over $1,400 today to be able to pay the rent for his business and still have some money left over.

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

• 
• 
• 
• 

Bam bought 4 mangoes and 7 guavas. The total amount she paid was at least RM 230. If 𝑥 represents the cost of each mango and 𝑦 the cost for each guava, which of the following mathematical statements represents the given situation?

• 4𝑥 + 7𝑦 ≥ 230

• 4𝑥 + 7𝑦 ≤ 230

• 4𝑥 + 7𝑦 > 230

• 4𝑥 + 7𝑦 < 230

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

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

It takes Sarah 2 hours to make small purses (x) and 3 hours to make big purses(y). She can work for no more than 18 hours a week. Which inequality represents this situation?

• 2x + 3y ≤ 18

• x + y ≤ 6

• x + y ≤ 9

• 3x + 2y ≤ 18

A restaurant owner would like to make a model which he can use as a guide in writing a linear inequality in two variables. He will use the inequality in determining the number of kilograms of pork and beef that he needs to purchase daily given a certain amount of money (C), the cost (A) of a kilo of pork, the cost (B) of a kilo of beef. Which of the following models should he make and follow?

• I and II

• I and III

• II and III

• I, II, and III

Nerolin is selling bracelets and earrings on Etsy to make money for summer vacation. The bracelets (x) cost $2 and earrings (y) cost $3. She needs to make at least $100, but can only make up to 40 pieces of jewelry. Which inequalities represent this situation?

• 2x + 3y > 100

  x + y ≤ 40

• 100x + 2y > 3

  x + y ≤ 40

• 100x + 40y > 100

  3x + 2y ≤ 40

• 3x + 2y > 100

  x + y ≤ 40

A store sells AirPods (a) and makes a $75 profit on the sale of each one. They also sell Apple Pencils (p) and they make $30 profit on those. The store wants to make a profit off these two items of at least $255. Which inequality describes this situation?