Framing/Writing Linear Inequalities in Two Variables

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?

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?

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

The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school would like to sell 3 senior citizen tickets and 2 child tickets for a total at least $42. Write an inequality that represents this situation.

A theater wants to take in at least $2000 for a certain matinee. Children’s tickets (x) cost $5 each and adult tickets (y) cost $10 each.

• $5x + $10y ≥ $2000

• $5x + $10y < $2000

• $15(x+y) ≥ $2000

• $2000 - $5x < $10y

There are two classrooms available for the upcoming debate tournament. Room A has a capacity of 28 and room B has a capacity of 35. If there are at most 253 students participating in the tournament, write an inequality to represent how many possible sessions there would have to be, given that both rooms could be used? Let a represent room A and b represent room B.

• 28a + 35b − 253 = 0

• 28a + 35b ≥ 253

• 28a + 35b ≤ 253

• 253 + 28a = 35b

Bam bought 4 mangoes and 7 guavas. The total amount she paid was at least $23. 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 ≥ 23

• 4𝑥 + 7𝑦 ≤ 23

• 4𝑥 + 7𝑦 > 23

• 4𝑥 + 7𝑦 < 23

Aleris is sending a fancy organic fruit basket to her grandma for her birthday. Apples cost RM3 and oranges cost RM2. Aleris can spend no more than RM24 on the gift. Write an inequality that describes the situation. Let x = # of apples Let y = # of oranges

• 3x + 2y < 24

• 3x + 2y ≤ 24

• 3x + 2y > 24

• 3x + 2y ≥ 24