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 grill at a barbecue restaurant will be used to cook sausage links that are 2 lb each and briskets that are 6 lb each. No more than 120 lb of sausage links and briskets will be cooked on the grill. Write an inequality that represents this situation.

Tickets for lower deck seats cost $42 each and tickets for upper deck seats cost $30 each. Which inequality represents the combinations of x, the number of tickets for the lower deck, and y, the number of tickets for the upper deck, that someone can buy for no more than $800?

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.

• $6x+3y\le30$

• $6x+3y\ge30$

• $3x+6y<30$

Luka and Dana are making cookies for the Westland Pantry. They only have up to 6 hours to bake! They can bake 32 chocolate chip cookies in an hour (x), and 20 snickerdoodle cookies in an hour (y). They need to make at least 150 cookies. Which inequalities represent the situation?

•  $x+y\ge6$  
   $32x+20y\le150$  

•  $x+y\ge32$  
   $x+20y\ge150$  

•  $x+y\le6$  
   $32x+20y\le150$  

•  $x+y\le6$  
   $32x+20y\ge150$  

In football, a kicker can score one point for the extra point on a touchdown or three point for a field goal. Logan is a kicker for his high school football team. The record number of point scored by a kicker in a single game is 24. Logan is hoping to beat his record in his next game.

Write a linear inequality to represent this situation in standard form.

Angela wants to spend less than $200 on condiments. Each kilogram of salt costs $30, and each kilogram of pepper costs $90. Write an inequality that represents the number of kilograms of salt (s) and pepper (p) Angela can buy on her budget.

• 30s + 90p > 200

• 30s + 90p ≥ 200

• 30s + 90p < 200

• 30s + 90p ≤ 200

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

A school is organizing a fundraiser by selling tickets for a concert. The school wants to make at least $1000 from the ticket sales. They are selling student tickets(s) for $5 each and adult tickets(a) for $10 each. Write a linear inequality to represent this situation.

• 5s - 10a ≥ 1000

• 5s - 10a ≤ 1000

• 5s + 10a ≥ 1000

• 5s + 10a ≤ 1000