1. Real World Situations

2. Table of Contents
49: Worksheet
48: Warm-Up,

3. Warm-Up/Quiz
Solve the following inequality for the variable. Write the answer in set notation and graph the solution on a number line:
1. 4x – 3 > m + 5 ≥ h + 4 ≥ – 7y < 33

4. Learning Intention/Success Criteria
LI: We are learning to solve inequalities in real world situations SC: I know how to -write inequalities and equations from word problems -write solutions to inequalities using set notation -solve two step equations algebraically -compare data and solutions -answer inequalities in context

5. Worksheet
5/4/2019

6. Worksheet #1
Sharon needs to move tomorrow for her new job. She rents a U-Haul truck to move her belongings. It costs $30 to rent the truck she needs, plus $0.50 per mile to rent the truck she needs. Let P(m) be the price of renting the truck and driving it for m miles.

7. Worksheet #1a, #1b A] Write the symbolic representation of P(m)
P(m) = 0.5m + 30
B] Sharon has budgeted $200 for the truck rental. How many miles can she drive on her budget? To find the answer, solve for m such that P(m) ≤ Represent your answer in Set Notation
{ m : m ≤ 340 }

8. Worksheet #1c { m : m < 140 }
C] Sharon wanted to save money, so she went online to find alternative truck rental companies. She found that Freddy’s garage can rent her a truck for a flat rate of $100. So, she wants to compare under what conditions it will be cheaper for her to rent from U-Haul versus Freddy’s garage. Solve for m, such that P(m) < 100 to find the answer. Represent your answer in set notation.
{ m : m < 140 }

9. Worksheet #1d
D] Sharon computers the distance she will need to drive during the move. She determines that she will drive 120 miles. Should she rent from U-Haul or from Freddy’s garage? Explain your answer.
U-Haul is cheaper because if she travels 120 miles, it will only cost her $90. However, if she rented from Freddy’s, it would be $100, no matter how many miles she drives. If she were to drive over 140 miles, then Freddy’s would be the better deal.

10. Worksheet #2
When mobile (cell) phones became popular around the year 2000, people had to purchase a text message plan. Back then, a company offered 2 text messaging plans that customers could choose:
Plan A charges a monthly fee of $5.00 plus $0.10 per text
Plan b charges a monthly fee of $10.00 plus $0.05 per text

11. Worksheet #2a
A] Let A(t) be the cost of Plan A if t texts are used. Write the symbolic representation of A(t).
A(t) = 0.1t + 5
B] Let B(t) be the cost of Plan B if t texts are used. Write the symbolic representation of B(t).
B(t) = 0.05t + 10

12. Worksheet #2c
C] In the context of the given situation, explain what the inequality A(t) < B(t) is really asking.
It is asking, how many text messages can be sent so that Plan A is cheaper than Plan B?

13. Worksheet #2d
D] Set up and solve the inequality A(t) < B(t) using the functions you created in 2a and 2b.
t < 100
E] Explain what your solution above (2d) means in context of the given situation
t < 10 means that Plan A will be cheaper than Plan b if you send less than 10 text messages in a month

14. Worksheet 2f
F] If a customer estimated they would send about 200 texts per month, which plan (A or B) should they choose? Explain why you decided that plan would be best.
Plan A would be the better deal because it is cheaper by $5.

15. Worksheet 2g
G] Kyla’s parents said they would pay, at most, $20 per month for her texting plan. If her parents selected Plan A, how many texts can she send without going past the $20 limit? Set up and solve an inequality using the function you created for Plan A.
As long as Kyla sends under 150 texts, she will be within her parents budget of $20