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

2023
Views:

401

Pages:

1
Author:

Isabella Bolton

Mini-Lecture 2.6 Formulas and Problem Solving Learning Objectives: 1. Use formulas to solve problems. 2. Solve a formula or equation for one of its variables. Examples: 1. Substitute the given values into each given formula and solve for the unknown variable, If necessary, round to one decimal place. a) Distance Formula d = rt; t = 9, d = 63 b) Perimeter of a rectangle P = 2l + 2w; P = 32, w = 7 c) Volume of a pyramid 1 V = Bh; V= 40, h = 8 3 d) Simple interest I = prt; I = 23, p = 230, r = 0.02 e) Convert the record high temperature of 102°F to Celsius. (F = 9 C + 32 ) 5 f) You have decided to fence an area of your backyard for your dog. The length of the area is 1 meter less than twice the width. If the perimeter of the area is 70 meters, find the length and width of the rectangular area. g) For the holidays, Chris and Alicia drove 476 miles. They left their house at 7 a.m. and arrived at their destination at 4 p.m. They stopped for 1 hour to rest and re-fuel. What was their average rate of speed? 2. Solve each formula for the specified variable. a) Area of a triangle 1 A = bh for b 2 b) Perimeter of a triangle c) Surface area of a special rectangular box S = 4lw + 2 wh for l d) Circumference of a circle C = 2πr for r P = s1 + s2 + s3 for s3 Teaching Notes: • • • • Most students will only need algebra reminders when working with a formula given values. Refer students to Solving Equations for a Specified Variable chart in the textbook. Most students have problems with applications. Refer them back to section 2.4 and the General Strategy for Problem Solving in the textbook. Each section in the text has 3 worksheets in the Extra Practice featuring differentiated learning. Answers: 1a) 7; 1b) 9; 1c) 15; 1d) 5; 1e) 38.9°C; 1f) l=23, w=12; 1g) 59.5 mph; 2a) b = 2b) s3 = P − s1 − s2 ; 2c) S − 2wh C ; 2d) r = 4w 2π 2A ; h