Writing Inequalities

The temperature in the ice rink must stay below 50°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. Which inequality shows how long it will take for the temperature to fall below 50°F?

• 50 + 3.5x < 71
• 71 - 3.5x < 50
• 71 - 3.5x ≤ 50
• 71 + 3.5x < 50

The vet told Casey that her dog should weigh at most 70 lbs. Her dog weighs 106 pounds, so Casey set a goal that he would lose 4 pounds per week. Which inequality represents the number of weeks it take for Casey's dog to reach 70 lbs?

• 106 - 4x ≤ 70
• 70 + 4x ≤ 106
• 4x - 106 ≥ 70
• 106 - 4x< 70

The members of YJH cheerleaders need to raise at least $2000 to attend their national competition. They raised $300 with their last fundraiser and decide to host a school talent show to raise the rest. They plan to charge $10 for each ticket. Which inequality shows the number of tickets they must sale to reach their goal?

• 300x + 10 ≥ 2000

• 10x + 300 ≤ 2000

• 10x + 300 > 2000

• 300 + 10x ≥ 2000

Juan bought a soda for $2. He also bought some nachos for $3 each. Juan did not spend more than $14 on the nachos and the soda. Write an inequality can be used to find n, the number of nachos that Juan could have bought.

• 14 ≥ 2n+3

• 2+3n ≤ 14

• 14-3n ≤ 2

• 14x+2 ≤ 3

Alexa has at most $60 to spend on the clothes. She wants to buy a pair of jeans for $22 and spend the rest on t-shirts. Each t-shirt cost $8. Write an inequality that could be used to find x, the number of t-shirts Alexa can buy.

• 60≥22x-8

• 22-8x≥60

• 22x+8≤60

• 22+8x≤60

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?

At the Big Bear video rental store, blank CDs cost $1.50 each and blank DVDs cost $3.25 each. Which of the following statements best describes the number of CDs (c) and DVDs (d) that can be purchased for less than $65.00?

• 1.50c + 3.25d < 65

• 3.25c + 1.50d <65

• 1.50c + 3.25d ≤ 65

• 3.25c + 1.50d ≤ 65

A donut shop charges $0.70 for each donut and $0.30 for a carryout box.  Shirley has $5.00 to spend.  She needs to determine the most donuts (x) she can buy when she only puts them in one carryout box.  Which equation can be used to answer this problem?

• 70x + 30 < 500
• 30x + 70 < 500
• 70x + 30 ≤500
• 30x + 70 ≤ 500

A local bakery has a daily operating cost of $1800 plus a cost of $10 per cake they make. If a cake sells for $15, which equation could be used to determine the minimum number of cakes, c, they must sell each day to earn a profit?

• 15c < 1800 + 10c

• 15c > 1800 + 10c

• 15c = 1800 + 10c

• 10c < 1800 + 15c

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