Problem Solving Strategy s2

Problem Solving Strategy Make an Organized List or Chart

Example 1 Like many early bicycles, the Boneshaker had different sized wheels. Suppose the circumference of the wheels were 4 ft and 18 ft. How many revolutions would each wheel make before marks on their rims would both be in the same positions again?

Analyze – What are you asked to find? What information are you given?

Choose – What strategy will you use? You can use the strategy make an organized list. List the total distance traveled by each wheel for every complete turn.

Solve – How will you solve the problem? Make a list of multiples of 4 and 18. Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40 Multiples of 18: 18, 36, 54

The least common multiple is 36. When the wheels have traveled 36 ft, the marks will both be in the same positions again. 36 is the ninth multiple of 4, so the small wheel makes 9 revolutions.

36 is the second multiple of 18, so the big wheel makes 2 revolutions.

Check – How can you check your answer? What if the smaller wheel had a circumference of 8ft? How many revolutions would each wheel make before the marks were both in the same position again?

Example 2 The 5 members of the Montoya family are planning their next vacation. They will travel in June or July to San Diego, Lake Tahoe, Los Angeles or San Francisco. How many different vacations involving one place and one month are possible?

Guided Practice 1. 1. Justin and Amy help with the shopping for their individual families Justin goes to the store every 3 days and Amy goes to the store every 5 days. They see each other at the store on September 30. On what date will Justin and Amy see each other at the store again? 2. Mrs. Chen is making a dental appointment. It can be on Monday, Tuesday, Wednesday or Thursday at 9:30am, 11:00am, or 2:00 pm. How many choices does Mrs. Chen have?

Making an organized list – homework problems 1. Gilbert is packing for a ski trip. He has 2 jackets, 2 pairs of ski pants and 2 hats. How many different outfits can Gilbert make if each outfit consists of a jacket, pants and a hat?

2. A dance company performs in non-overlapping groups of 8 and 10. There are 64 dancers in all. There are more groups of 10 than groups of 8. How many groups of each size are there?

3. Laura wants to buy the same number of plums and kiwis. Plums are sold in bags of 4 and kiwis are sold in bags of 7. How many bags of each fruit does Laura need to buy in order to have the same number of plums and kiwis?