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

2023
Views:

337

Pages:

1
Author:

Marilyn James

Mini-Lecture 7.6 Proportion and Problem Solving with Rational Equations Learning Objectives: 1. 2. 3. 4. 5. Solve proportions. Use proportions to solve problems. Solve problems about numbers. Solve problems about work. Solve problems about distance. Examples: 1. Solve each proportion. x 6 2 5 = = a) b) 39 13 7 x c) 8+ x 5+ x = 5 3 d) 7 z−5 = 2 z−3 2. Solve. Find the unknown length (x) in the pair of similar triangles. a) There are 170 calories in 3 peanut butter cookies. How many calories are in 7 cookies? b) 21 18 27 14 28 x 3. Solve the following: problems about numbers. a) Five divided by the difference of a number and one equals the quotient of ten and the sum of the number and twelve. Find the number. b) If three times a number added to five is divided by the number plus nine, the result is four thirds. Find the number. 4. Solve the following: problems about work. a) A painter can paint a sign in 4 hours. His assistant can paint the same sign in 6 hours. How long will it take them to paint the sign if they paint it together. b) A conveyer belt can move 1000 cans of soup to the loading area in 7 minutes. A smaller conveyer belt can move the same number of cans in 11 minutes. How long will it take to move 1000 cans of soup if both conveyer belts are used. 5. Solve the following: problems about distance. a) A cyclist bikes at a constant speed for 18 miles. His return trip is a different route of 23 miles long and will take 1 hour longer. Find the speed. Teaching Notes: • • • Most students will struggle with applications. Refer students to Chapter 2, Section 2.4, General Strategy for Problem Solving. Each section in the text has 3 worksheets in the Extra Practice featuring differentiated learning. Answers: 1a) 18; 1b) 35/2; 1c) -1/2; 1d) 11/5; 2a) 396⅔; 2b) 36; 3a) 14; 3b) 21/5; 4a) 2.4 hours; 4b) 4 5/18 min.; 5a) 5 mph.