University:
Montgomery College
Course:
MATH 130: Elements of Mathematics I: Mathematical Reasoning and Number Systems
Academic year:

2023
Views:

423

Pages:

1
Author:

Carina Becker

Mini-Lecture 2.5 An Introduction to Problem Solving Learning Objectives: Apply the steps for problem solving as we 1. Solve problems involving direct translation. 2. Solve problems involving relationships among unknown quantities. 3. Solve problems involving consecutive integers. Examples: 1. Solve. a) Eight is added to a number and the sum is doubled, the result is –11 less than the number. Find the number. b) Three times the difference of a number and 2 is equal to 8 subtracted from twice a number. Find the integers. 2. Solve. a) A college graduating class is made up of 450 students. There are 206 more girls than boys. How many boys are in the class? b) A 22-ft pipe is cut into two pieces. The shorter piece is 7 feet shorter than the longer piece. What is the length of the longer piece? c) A triangle has three angles, A, B, and C. Angle C is 18° greater than angle B. Angle A is 4 times angle B. What is the measure of each angle? (Hint: The sum of the angles of a triangle is 180°). 3. Solve. a) The room numbers of two adjacent hotel rooms are two consecutive odd numbers. If their sum is 1380, find the hotel room numbers. b) When you open a book, the left and right page numbers are two consecutive natural numbers. The sum of their page numbers is 349. What is the number of the page that comes first? Teaching Notes: • • • • • Many students find application problems challenging. Encourage students, whenever possible, to draw diagrams, charts, etc. Encourage students to use algebra to solve a problem even though they may be able to solve without it. Refer students to General Strategy for Problem Solving section 2.4. Each section in the text has 3 worksheets in the Extra Practice featuring differentiated learning. Answers: 1a) -27; 1b) 21, 63; 2a) 122 boys; 2b) 14.5 feet; 2c) A=108°, B=27°, C=45°; 3a) 689, 691; 3b) 174