Unit 6 Box D Writing Inequalities

Baseball Hats You are a big baseball fan. You have a goal of attending a baseball game in every major league stadium in the country. Every time you go to a different stadium, you buy a baseball hat. You keep your hats in a display case that holds 25 hats. You have 8 baseball hats so far. What are the possible numbers of hats you can collect without needing another display case?

• 17 hats or less

• more than 17 hats

• 33 hats or less

• more than 33 hats

Gift Card You received a $25 gift card to a sporting goods store for your birthday. You are looking at skateboards and want to spend no more than $85 of your own money.

a. Write and solve an inequality to find the prices p in dollars of skateboards you can buy.

b. What is the most expensive skateboard you can buy?

• a. p + 25 ≤ 85; p ≤ 60

  b. A $60 skateboard

• a. p – 25 > 85; p > 110

  b. A $110 skateboard

• a. p – 25 ≤ 85; p ≤ 110

  b. A $110 skateboard

Pavilion Rental You and three of your friends decide to rent a pavilion at a local park for an end-of-the-school-year party. The group budget is $80. The group decides to split the cost equally.

a. What are the possible amounts of money that each of you can spend?

b. If two more of your friends decide to pitch in for the party, what are the possible amounts of money that each of you can spend if you all split the cost equally?

• a. $40 or less b. about $28 or less

• a. $20 or less b. about $13.33 or less

• a. $26.70 or less b. about $5 or less

Waiting Tables Restaurants typically pay wait staff an hourly wage that is lower than minimum wage. The wait staff is expected to make up the difference in tips. The minimum wage is $5.15 per hour and a restaurant pays the wait staff $4 per hour.

a. If a waitress works an 8-hour shift, write and solve an inequality that gives the total tips t in dollars that the waitress must earn in an 8-hour shift in order to meet or exceed the minimum wage.

b. If the waitress makes $10.40 in tips during an 8-hour shift, will she meet or exceed the minimum wage? By how much?

• t/8 ≥ 5.15; t ≥ 41.2 b. yes; by $4.20

• a. t/8 ≥ 1.15; t ≥ 9.2 b. yes; by $1.20

School Spirit Your club is in charge of making pins that students can buy to show their school spirit for the upcoming football game. You have made 225 pins so far, and you only have 2 hours left to make the rest of the pins. You need to make at least 400 pins.

a. Write an inequality that gives the possible numbers p of pins you have to make per minute in order to exceed your goal.

b. What are the possible numbers of pins you have to make per minute in order to exceed your goal?

• a. 225 + 120p ≥ 400 b. 2 pins or more

• a. 225 + 120p ≤ 400 b. 2 pins or more

• a. 225 + 120p < 400 b. 2 pins or less

Aquarium You are getting a larger aquarium for your neon tetra fish and you also want to add more neon tetras to the larger aquarium. The general rule is that each fish needs 2 gallons of water. You currently have 6 neon tetras. If you buy a 20-gallon aquarium, what are the possible numbers of fish you can put in your aquarium?

• 8 fish or less

• 4 fish or more

• 4 fish or less

• 8 fish or more

Temperature The high temperature in a city last year was 95°F. The low temperature in this city last year was –5^oF. Write and graph a compound inequality that represents the temperatures T throughout the year.

• –5 ≥ T ≥ -95

• –5 ≥ T ≥ 95

• 5 ≤ T ≤ 95

• –5 ≤ T ≤ 95

Keith has $500 in a savings account at the beginning of the summer. He wants to have at least $200 in the account by the end of the summer. He withdraws $25 each week for food, clothes, and movie tickets.

Write an inequality that represents Keith's situation. How many weeks can Keith withdraw money from his account? Justify your answer.

• w ≤ 12

• w ≤ 1

• w ≥ 12

• w ≤ -12

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 a ride.

Write an inequality that represents Katie's situation. How many miles can Katie travel without exceeding her budget? Justify your answer.

• m ≥ 18.07

• m ≤ 18.07

• m ≤ -12.69

• m ≤ 12.69

Skyzone charges a $50 flat fee for birthday party rental and $5.50 per person. Joann has no more than $100 to spend on the birthday party.

Write an inequality to represents Joann's situation. How many people can Joann invite to her birthday party without exceeding her limit of $100?

• p < 9

• p > 9

• p < 28

• p > 28