Solving Inequalities Story Problems

Yellow Cab Taxi charges a $1.75 flat rate in addition to $0.65 per mile.  Katie has no more than $10 to spend on the taxi ride.

• 1.75 + 0.65m < 10

• 1.75 + 0.65m > 10

• 1.75m + 0.65 < 10

• 1.75m + 0.65 > 10

Svetlana's hair is 4 centimeters long. Her hair grows 1.5 centimeters per month. Svetlana wants her hair to grow so that it is at least 7 centimeters long. Write an inequality to determine the number of months, m, it will take Svetlana's hair to grow so it is at least 7 centimeters long.

• 4+ 1.5m <= 7

• 1.5m - 4 <=7

• 1.5m - 4>= 7 

• 1.5m + 4 >= 7

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?

Suzy is buying In-N-Out Burger for lunch for her friends.  The hamburgers cost $3.50 each and the drinks cost $1.50 each.  She wants to spend no more than $30 on lunch.  What inequality represents the number of hamburgers, h, and number of drinks, d, that she can buy?

• 3.5h + 1.5d ≤ 30

• 3.5d + 1.5h ≤ 30

• 3.5h + 1.5d ≥ 30

• 3.5h + 1.5d < 30

Cody’s Gym charges a $18 fee to join and $30 per month. Tyler’s Gym charges a $50 fee to join and $20 per month. Use an inequality to determine how many months will you have to go to the gym before Tyler’s gym becomes the better deal.

• 3

• 4

• 5

• 6

To qualify for an award, a student volunteers no less than 5 hours each week at the local hospital. Write an inequality that represents how many hours the student volunteers each week.

• X < 5

• X > 5

• X ≥ 5

• X ≤ 5

You and your friend are planning to walk across an old bridge. The bridge can hold at most 1000 pounds. The total weight of the people currently on the bridge is 675 pounds. You weigh 156 pounds.Write and solve an inequality that represents how much your friend can weigh within the limits of the bridge.

• X ≤ 169 

• X < 169

• X < 156

• X > 156 

You order a new pair of running shoes from a website that offers free shipping on orders of $75 or more. Your shoes cost $69.95. Write and solve an inequality that represents how much more you must spend to get free shipping. 

• X > 5.05

• X ≥ 5. 05

• X > 69.95

• X ≥ 69.95

You bike for 2 hours at a speed no faster than 17.6 miles per hour. Write and solve an inequality that represents the possible numbers of miles you bike.

• X ≤ 17.6

• X ≥ 17.6 

• X ≥ 35.2 

• X ≤ 35.2

The speed limit is 45. Katie was going thirty miles per hour and sped up some. Which inequality represents the amount she could speed up and not be speeding?

• 30 + s ≥ 45

• 30 - s ≥ 45

• 30 + s ≤ 45

• 30 - s ≤ 45