Activities

1. The inequality 40w + 100 ≥ 1000 represents Nick’s saving account. He started his savings account with his $100 of birthday money. Every week thereafter he deposits $40 into his account. Solve the inequality and determine how many weeks it will take Nick to reach his goal of $1000.

2. A prospective homeowner wants to buy a house with a rectangular pool that has an area of at least 450 ft². If one of the houses has a pool with a length of 12 feet, what must the width be in order to meet the buyers demand?

3. Write and solve an inequality used to determine how to cut a length of rope into 3, three-foot lengths and 5, one and a half lengths. If the rope is sold only by the foot, at least how long (l) will the original rope need to be?

4. Your new car travels 23 miles for each gallon of gas. You are planning to visit a friend 300 miles away, and already have 4 gallons of gas in the car. Write and solve an inequality used to determine how many gallons of gas (g) you need to buy to get to your friends house.

5. Over the course of the summer, Mary was able to save $2345.00 from her job as a waitress. She has already budgeted $200.00 to buy gifts for her friends and family. Write and solve an inequality that could be used to determine how much money (m) she can spend during each of the 40 weeks in the school year so that she will not run out of money before next summer.

6. A certain type of vegetable will grow at a rate of at least 0.5 inches per day. Is it possible for the plant to be 11.25 inches 23 days after emerging from the ground?

7. One lap around a regulation running track is 400 meters. Elijah can run one lap around the track in one minute and eleven seconds. Estimating that one-mile is approximately 1600 meters; do you think Elijah could run three miles in 15 minutes? Explain your reasoning.

8. A box truck that Tiffany is using to move to a new apartment in Erie, PA, has a volume of 640 ft³. Assuming that all of Tiffany’s things fit into boxes that have a volume of 15 ft³ each, how many boxes (b) can fit into the box truck?

9. Tom has $20.00 to spend on books at a used bookstore. He must buy one book for school and then can purchase as many western’s as he can afford. The book for school costs $7.00 and each of his favorite western’s are $1.50. Write and solve an inequality that would determine how many western’s (w) Tom could buy. Why can’t you round your final answer?

10. If the inequality graphed on the number line below represents the grade Jose needs to earn on the final exam in order to pass his English class for the year, what is the lowest grade Jose can receive and still pass the course.

11. Josh has $45 budgeted for his outing to the amusement park. One attraction charges a flat fee of $18.50 and $7.50 for each 10 minutes in the attraction. Write and solve an inequality that will determine (G) the number of minutes Josh can afford.

12. Ruby and her friend Sapphire were determining how many minutes it took for their math teacher to get to school. Their teacher told Ruby it took m ≥ 7 minutes to get to school. Meanwhile, he secretly told Sapphire it took him 7 ≥ m to get to school. Exactly how long did it take him to get to school?

13. The inequality 0.75m + 2.5 ≤ c describes Yellow Car, a taxi company’s, cost for a trip that Austin is taking. Yellow Car includes a flat fee and a cost per mile. What is the charge per mile and the flat fee for using Yellow Car. If Austin has $20 to spend on his taxi ride, how far can he travel? Use the above inequality to show your work.

14. David is buying packs of new socks to prepare for the school year. The packs are $5.85 each without the 6% sales tax. If Dave has $50 to spend on socks, how many packs can he purchase if he needs to give $20 dollars to his wife and pay sales tax on the socks. Write and solve an inequality to show your answer.

15. Pam has a special rewards card at her favorite coffee shop. If she earns 100 points throughout the year she can receive a $20 gift card for the next year. To earn 5 points, Pam needs to spend $15. How much does she need to spend in order to receive the gift card? Write and solve an inequality to show your answer.

16. A person’s income (i) can be taxed at a rate of 30%. If you want to take home (after taxes) a salary of $50,000, how much gross income will you need to make in order to achieve your goal? Write two different inequalities that represent this situation.

17. The local restaurant sells burgers for $2.50, hot dogs for $2.00, fries for $2.00, salads for $1.75 and iced tea for $1.25. If your group of 5 friends goes to the restaurant with $30.00 to buy 2 burgers, 3 fries, and 4 salads, what is, in your opinion, the best way for them to spend the rest of their money on hot dog’s and iced tea so that they have the least amount of change left over. Write an inequality to represent this situation and use the inequality in your explanation.

18. Nick is up late trying to finish reading The Great Gatsby for English class. He already read 268 of 351 pages before this night. Nick has either 3 or 4 hours to finish reading the book. Using the inequalities 3p + 268 ≥ 351 and 4p + 268 ≥ 351 determine how many pages per hour more he will have to read in order to finish the book in 3, versus 4 hours?

19. If you find the sum of the ages of the four people in Martha’s family the result is greater than 130 years. Currently, Martha’s mother is 31 years older than Martha. Her father is 4 years older than her mother. Martha’s younger sister is 37 years younger than her father. Martha is, at the least, how old?

20. At a certain amusement park, a person must be 55” tall in order to ride the most extreme roller coasters. Hamidah was 26” tall when she was 2 years old and has grown at an average rate of 1.85 inches per year since that time. Write and solve an inequality that can be used to determine the age (a) when Hamidah will be able to ride the roller coaster. How old will she be?

21. At the beginning of the school year, Frank is assigned to take the yearbook pictures for 455 students at Lewistown High School. Based on experience Frank knows that he will take no more than 23 seconds to take the picture of each student. If he has only three and a half hours to be at the school, write and solve an inequality that determines the amount of minutes (m) that Frank will have at the school when he is not taking pictures.

22. Josh, Bryan and Luke all went to the county fair on Friday night for the food and games. Luke spent (d) dollars at the fair. Bryan spent double the amount of money as Luke did. Josh spent half as much money as Luke. If they spent over $38.00 altogether, then what is the least amount of money Josh could have spent. Write and solve an inequality to find your solution.

23. A certain non-profit organization is trying to raise at least $100,000 for a new building. An extremely generous donor has pledged to pay double the amount of any contribution during the next month. How much money (m), not from the matching donations, does the organization need to raise in order to pay for the building. Write and solve an inequality to determine your solution.

24. A car wash is offering a special in addition to their regular prices. The special requires you to pay $45.00 and you get unlimited free washes for the year. The regular price is $3.75 per wash. Write and solve an inequality to determine at what number of washes it would be better to get the special offer.

25. A basketball team is buying new jerseys. Star-screen printing charges $40 per jersey and a $50 logo design fee. Meanwhile, New Jerseys charges only $45 per jersey. At what point would it be cheaper to use Star-screen printing instead of New Jerseys. Use two inequalities to show your work.

Answer Key/Rubric

1. 23 weeks

2. 38 feet

3. l ≥ 17 feet

4. 23g + 4(23) ≥ 300, g ≥ 9.04, 10 gallons of gas

5. 40m + 200 ≤ 2345, m ≤ 53.62 , $53.62 spend per week

6. No, it will be at least 11.5 inches

7. Various answers, if he keeps that pace, Elijah could run three miles in 14:12. If you assume he slows down when running a longer distance, then he might not be able to do it.

8. b ≤ 42 boxes

9. 1.5w + 7 ≤ 20, w ≤ 8.67, Tom can only buy 8 books because he does not have enough money to buy the 9^th book, you cannot round up because they will not sell the 9^th book for only $1.

10. Jose needs to score higher than an 83%, that could mean he would get an 84% or some students may answer that he would get some decimal or fractional value greater than 83%, but NOT 83% exactly

11. 7.5G + 18.5 ≤ 45, G ≤ 3.53, 3.53x10 =35.30, 30 minutes on the ride

12. 7 minutes

13. Flat fee: $2.50, $0.75 dollars per mile, he can travel 23 miles

14. 1.06(5.85p) + 20 ≤ 50, p ≤ 4.83, 4 pairs of socks

15. , x ≥ 300, spend $300 to get gift card

16. i – 0.3i ≥ 50,000 or 0.7i ≥ 50,000, i ≥ $71,428.57

17. 2(2.5) + 3(2) + 4(1.75) + 2h + 1.25i ≤ 30, various answers for the best way to spend including 4 iced teas and 3 hot dogs.

18. He will have to read at least 6.9 pages per hour faster to finish in 3 hours instead of 4 hours

19. Martha is at least 17 years old

20. (a – 2)1.85 + 26 ≥ 55, she will be 18 years old

21. 455(23) + (60m) ≤ 3.5(60)(60), Frank will have at least 35 minutes of free time

22. d + 2d + 0.5d > 38, Josh spent at least $5.43 at the fair

23. m + 2m  ≥ 100,000, at least $33,333 during the next month

24. 3.75x > 45, you would need 13 car washes during the year to benefit from the special offer
    
    
25. 40x + 50 < 45x, it would be cheaper to use Star-screen if you were buying at least 11 jerseys