Framing/Writing Linear Inequalities in Two Variables from Word Problem

Which of the following inequalities illustrate “the sum of 𝑥 and 𝑦 is at most 15”?

• 𝑥 + 𝑦 = 15

• 𝑥 + 𝑦 > 15

• 𝑥 + 𝑦 ≤ 15

• 𝑥 + 𝑦 ≥ 15

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.

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

Sam's uncle gives him a $50 gift card to a digital store. Songs cost $1.99 each and movies cost $6.99 each. Which inequality represents the number of songs and movies Sam can purchase?

Angela wants to spend less than Php 200 on condiments. Each kilogram of salt costs Php 30, and each kilogram of pepper costs Php 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