Practical Inequalities

Which situation can be represented by the inequality
15 + 6x ≤ 100?

• Lazer Zone charges $15 plus $6 per person. If Andrea has a maximum of $100 to spend, how many people can Andrea invite to play laser tag?

• Lazer Zone charges $6 plus $15 per person. If Andrea has a maximum of $100 to spend, how many people can Andrea invite to play laser tag?

• Lazer Zone charges $15 plus $6 per person. If Andrea has a minimum of $100 to spend, how many people can Andrea invite to play laser tag?

• Lazer Zone charges $6 plus $15 per person. If Andrea has a minimum of $100 to spend, how many people can Andrea invite to play laser tag?

Daniel can spend no more than $40 at the fair. If admission into the fair is $10 and the rides cost $1.50 each, which inequality represents the greatest number of rides Daniel can go on?

• 10x + 1.50 ≥ 40

• 1.50x + 10 ≤ 40

• 1.50x + 10 <40

• 10x + 1.50 < 40

Mrs. Scott decided that she would spend no more than $120 to buy a jacket and a skirt. If the price of the jacket was $20 more than 3 times the price of the skirt, which inequality represents the highest possible price of the skirt?

• 20x + 120 ≥ 3

• x/3 + 20 ≤ 120

• 3x + 20 ≤ 120

• 3x + 20 ≥ 120

The dance committee hired a DJ for the fall dance. The DJ charges $125 per hour in addition to $55 for an assistant. The committee wants to keep the total cost under $600. Which inequality represents the maximum amount of hours the DJ will play at the dance?

• 125x + 55 ≤ 600

• 125x + 55 ≥ 600

• 125x + 55 > 600

• 125x + 55 < 600

Triniti had $500 in a saving account at the beginning of the summer. She wants to have at least $200 in the account by the end of the summer. She withdraws $25 each week for food, clothes, and movie tickets. Which inequality represents her situation?

• 200 + 25x ≥ 500

• 500 + 25x ≥ 200

• 500 - 25x ≥ 200

• 500 - 25x ≤ 200

At the end of the day, vegetables at the farmer’s market sells for $3.00 a pound, and a basket costs $5.50. If Carol wants to buy a basket and spend no more than $10.00 total, how many pounds of vegetables can she buy?

• 3 + 5.5p < 10

• 10 > 5.5 - 3p

• 5.5 + 3p < 10

• 3p + 5.5 ≤ 10

A willow tree is 5.1 feet tall and grows at a rate of 2.5 feet a year. After how many years will the tree have reached no more than 60 feet tall?

• 5.1 + 2.5y ≥ 60

• 60 < 5.1 + 2.5

• 5.1 + 2.5y ≤ 60

• 5.1 + 2.5y > 60

The 30 members of a choir are trying to raise at least $1,500 to cover travel costs to a singing camp. They have already raised $600. Which inequality could you solve to find the average amounts each member can raise that will at least meet the goal?

• 30x + 600 > 1,500

• 30x + 600 ≥ 1,500

• 30x + 600 < 1,500

• 30x + 600 < 1,500

The temperature in the ice rink must stay at or below 40°F. This morning, the temperature was 71°F. The ice rink runs a cooling device that can decrease the temperature by 3.5° every hour. Let x represent the number of hours the cooling device was on. At least how long must the cooling device run?

• 40 + 3.5x < 71

• 71 - 3.5x < 40

• 71 / 3.5x < 40

• 71 + 3.5x < 40

Savannah spent $7 to buy supplies for a lemonade stand. She plans to sell each cup for $0.50. How many cups will Savannah need to sell to make more than $20

• 0.5x - 7 < 20

• 7x - 30 > 20

• 0.5x + 7 > 20

• 0.5x - 7 > 20