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

2023
Views:

354

Pages:

1
Author:

Kolten Khan

Mini-Lecture 4.4 Systems of Linear Equations and Problem Solving Learning Objectives: 1. Use a system of equations to solve problems. Examples: 1. Solve . a) Finding Unknown Numbers: The sum of two numbers is 7. Three times the first number equals 4 times the second number. Find the two numbers. b) Finding Unknown Numbers: One number is four more than a second number. Two times the first number is 2 more than four times the second number. c) Solving a Problem about Prices: Alicia purchased tickets to a local comedy club for 5 adults and 2 children. The total cost was $161. The cost of a child’s ticket was $7 less than the cost of an adult’s ticket. Find the price of an adult’s ticket and a child’s ticket. d) Solving a Problem about Prices: Allison throws loose change found in the laundry into container. After one month, she finds it contains all nickels and dimes. In fact, there are 4 times as many dimes as nickels, and the value of the dimes is $3.50 more than the value of the nickels. How many nickels and dimes does Allison have? e) Finding Rates: Kyle and Jason live 28 miles apart in Central Massachusetts. They decide to bicycle towards each other and meet somewhere in between. Kyle’ rate of speed is 40% of Jason’s. They start out at the same time and meet 2 hours later. Find Kyle’s rate of speed. f) Finding Amounts of Solutions: Amy has 3 liters of a 35% solution of sodium hydroxide in a container. What is the amount and concentration of sodium hydroxide solution she must add to this in order to end up with 7 liters of 27% solution? Teaching Notes: • • • • • • Most students struggle with word problems. Refer students to the textbook’s Problem-Solving Steps for guidance. Encourage students to draw and label diagrams or construct charts whenever possible. Entertain a discussion around which algebraic method, substitution or addition, is appropriate for the word problem. Remind students to always check their answer. Each section in the text has 3 worksheets in the Extra Practice featuring differentiated learning. Answers: 1a) 4,3; 1b) 7,3; 1c) $25, $18; 1d) 10 nickels, 40 dimes; 1e) 4 mph; 1f) 4 liters of 21% solution