UNIT 1 A Problem Solving Problem Solving Steps

UNIT 1 A Problem Solving

Problem Solving Steps 1. Understand the problem 2. Make a plan 3. Solve the problem 4. Check the solution

Problem #1 Keegan celebrated his birthday by inviting a group of friends to join in on having sundaes. The bill amounted to $27. 43. If the cost of each sundae was the same… a) How many friends did Keegan invite? b) What was the cost of the sundae?

Problem #2 Bob runs the elevator in an apartment building. He took Mr. Sloan up six floors from the one which he lives. Then Bob went down five floors, where he picked up Mrs. Rice. He took her down ten floors to the first -floor lobby. What is the number of the floor which Mr. Sloan lives?

Problem #3 If 4 * 3 = 24 8 * 2 = 32 and 1 * 5 = 10 what is the value of 6 * 7?

Problem #4 Mr. Smith has a rectangular vegetable garden. He decided to increase the size by making the length twice that of the original garden and the width three times that of the original garden. How many times as large as the original garden is the new garden?

Problem #4 The new garden will be 6 times as large as the original garden L W W W L

Problem #5 How many ways can change for a $20 bill be made in $1, $5, and/or $10 bills?

Problem #5 $1 $5 $10 # bills # bills 20 15 10 10 5 1 2 3 1 # bills 2 4 1 There are 8 different ways to make $20 using $1, $5, and $10 bills. # bills 2

Problem #6 At the end of an hour, a cook in a diner noted that one-third of the customers had ordered sandwiches, one-half had ordered hamburgers, one eighth had ordered steak, and the remaining two had ordered just a salad. If no customer ordered more than one of these items, how many customers were served?

Problem #6 Know 24 people? Sandwich 16 Hamburger 24 Steak Salad 48 people? 6 2 people 1 person 2 48 Total

What are some strategies you have used to problem solve?

Strategies • Guess and check • Use a simpler related problem • Working backward • Recognize patterns • Drawing pictures and diagrams • Making lists and charts

Problem #9 An auditorium seats 1, 073 people. Each row has the same number of seats, and there are more than 30 rows. a) How many rows are there? b) How many seats in each row?

Problem #9 •

Problem #13 Find the next number in the sequence 1, 3, 7, 15, 31, 63, 127, …

Problem #13 •

Problem #14 Sam planted some trees alongside his family’s driveway. If the distance from the first tree to the last tree was 200 feet and he planted the trees 50 feet apart, how many trees did he plant?

Problem #14 50 ft Sam planted 5 trees over 200 ft

Formulas • Evaluate a given formula by replacing variables with known values

Problem #1 •

Problem #2 •

Problem #3 •

Writing a Formula • Choose appropriate letters to represent each variable quantity and write what each letter represents • Use the letters to translate each stated relationship into a symbolic formula • Use the formula to solve the exercise

Problem #4 • Net pay is the difference between a worker’s gross income and his or her deductions. A peron’s gross income for the year was $65, 000 and their total deductions were $12, 860. What was their net pay for the year?

Problem #5 • Your goal is to save $1200 to pay for next year’s books and fees. How much must you save each month if you have 5 months to accomplish your goal?

Problem #6 In your part-time job, your hours vary each week. Last month, you worked 22 hours the first week, 25 hours the second week, 14 hours during week three, and 19 hours in week four. Your gross pay for those four weeks was $960. a) let p represent your hourly pay rate. Write the equation for your gross pay over these four weeks. b) Solve the equation in part a to determine your hourly pay rate.

• In your part-time job selling kitchen knives, you have two different sets available. The better set sells for $35, the cheaper set for $20. Last week, you solve more of the cheaper set, in fact twice as many as the better sets. Your receipts for the week totaled $525. How many of the better sets did you sell?

Ratios and Proprotions •

Problem #1 • Fill in the blanks in each of the following proportions • 3 out of 4 is equivalent to _____ out of 12 • 3 out of 4 is equivalent to _____ out of 32 • 3 out of 4 is equivalent to _____ out of 100

Proportional Reasoning •

Problem #2 •

Problem #3 • In an effort to increase the education level of their police officers, many municipalities are requiring new recruits to have at least a two-year college degree. A recent survey indicated that 1 out of 5 officers in the New York City Police Department (NYPD) holds a four-year college degree. There were approximately 41, 000 NYPD officers when the survey was conducted. How many NYPD officers held a four-year degree?

Problem #4 • New York State has taken a leading position in raising the standards of its high school graduates. In the year 2003, every graduate needed to pass a series of rigorous subject-matter tests called Regents exams. Currently, 6 out of 10 graduates receive Regents diplomas. If 5400 students in Buffalo earned a Regents diploma last year, find the total number of high school graduates in buffalo last year.