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

2023
Views:

181

Pages:

1
Author:

drolowpzco

Mini-Lecture 7.7 Variation and Problem Solving Learning Objectives: 1. 2. 3. 4. Solve problems involving direct variation. Solve problems involving inverse variation. Other types of direct and inverse variation. Variation and problem solving. Examples: 1. Write a direct variation equation, y=kx, that satisfies the ordered pairs in each table. a) x 0 2 5 7 y 0 10 25 35 x 0 5 -1 b) y 0 2 − 5 8 1 − 4 − 2 5 c) y varies directly as x. If y = 24 when x = 3 , find y when x is 6. 2. Write an inverse variation equation, y = a) x 1 2 4 8 y 4 2 1 0.5 k , that satisfies the ordered pairs in each table. x b) 3 10 0.05 x -2 y -0.15 0.1 0.03 6 c) y varies inversely as x. If y = 10 when x = 6, find y when x is 12. 3. Solve. 1 . 4 b) z varies inversely as a2. If z = 25 when a =2 , find z when a is 5. a) y varies directly as x2. If y = 72 when x = 3, find y when x is 4. Solve the following. a) Your paycheck (before deductions) varies directly as the number of hours you work. If your paycheck is $147.25 for 15.5 hours, find your pay for 24.5 hours. b) For a constant distance, the rate of travel varies inversely as the time traveled. If a truck driver travels 45 mph and arrives at a destination in 8 hours. How long will the return trip take traveling at 60 mph? Teaching Notes: • • • Most students understand direct variation but struggle with inverse variation. Most students struggle with the applications that involve both direct and inverse variation. Each section in the text has 3 worksheets in the Extra Practice featuring differentiated learning. Answers: 1a) y=5x; 1b) y = 4b) 6 2 4 0.3 1 x ; 1c) 48; 2a) y = ; 2b) y = ; 2c) 5; 3a) ; 3b) 4; 4a) $232.75; 5 2 x x