Linear Inequality Word Problems and Solutions with Two Variables

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

Write the linear inequality in standard form for this situation:

The CRHS science department can spend no more than $2700 on textbooks this year. The department needs to buy both Biology text books, which cost $57 each, and Chemistry textbooks, which cost $72 each.

• 57x + 72y ≥ 2700

• 57x + 72y > 2700

• 57x + 72y < 2700

• 57x + 72y ≤ 2700

Write the linear inequality in standard form for this situation:

A landscaping business is purchasing plants from a nursery to finish a project. It will cost $14 each to buy each tree and $5 each to buy each bush. The landscaper wishes to keep the spending under $1000.

• 14x + 5y ≥ 1000

• 14x + 5y < 1000

• 14x + 5y ≤ 1000

• 14x + 5y > 1000

Write the linear inequality in standard form for this situation:

In order to raise money to attend upcoming competitions, the Math Pentathlon team is selling apple cider and hot chocolate. They hope to make at least $240 by selling hot chocolate for $1 a glass and hot apple cider for $2 a glass.

• x + 2y < 240

• x + 2y > 240

• x + 2y ≤ 240

• x + 2y ≥ 240

Write the linear inequality in standard form for this situation:

The manager of an electronics store projects that the store should achieve more than $21,000 in revenue from TVs and DVD players every day in order to remain profitable. Tvs sell for $225 and DVD players sell for $175.

• 225x +175y ≤ 21,000

• 225x +175y ≥ 21,000

• 225x +175y < 21,000

• 225x +175y > 21,000

Addie saved more than $36. Which inequality represents the amount that she saved? 

• s > 36
• s < 36
• s ≤ 36
• s ≥ 36

Johnny earns $15 per hour for dog walking. He wants to earn at least $105 to buy a new bike. Which inequality represents how long Johnny needs to work to afford his new bike?

• 15h ≤ 105

• 15h > 105

• 15h < 105

• 15h ≥ 105

Pet Supplies makes a profit of $5.50 per bag on its line of natural dog food. If the store wants to make a profit of no less than $5225, how many bags of dog food does it need to sell?

• x/5.50 ≥ 5225

• 5.50x ≥ 5225

• x + 5.50 ≤ 5225

• x - 5.50 ≤ 5225

Two seventh-grade classes are selling raffle tickets to raise money.

One class is selling tickets for $3.50 each and has already raised $400.

The other class is selling tickets for $2.00 each and has already raised $300.

Which equation can be used to find m, the number of tickets each class needs to sell so that the total amount raised is the same for both classes?

• 5.5m = 700

• 3.50m = 2m + 300

• 3.5m + 400 = 2m + 300

• 3.5 + 400m = 2 + 300m

Renting games online from Netwii costs $3.33 per game with no monthly fee. Renting games online from HDO costs $2.00 per game plus a monthly fee of $10.00.

Which inequality represents the situation when the monthly cost at Netwii is more than the monthly cost at HDO?

• 3.33v > 2v + 10

• 3.33v + 10 > 2v

• 3.33v < 2v + 10

• 3.33v + 10 < 2v