Solving Word Problems with Equations

Lesson 29 focuses on solving word problems using linear systems of equations. The lesson includes multiple examples, such as finding two numbers based on their sum and difference, determining the number of boys and girls in a school, counting $5 and $1 bills, and calculating the cost of notebooks. Each example demonstrates how to define variables, set up equations, and solve them using methods like elimination and substitution. The lesson concludes with practice exercises to reinforce the concepts learned.

What is the first step in solving a word problem using linear systems of equations?

• Checking the answer

• Drawing a diagram

• Defining the variables

• Guessing the solution

In the school students problem, what equation represents the total number of students?

• x - y = 356

• x + y = 173

• x + y = 356

• x - y = 173

How many $5 bills are there if the total number of bills is 18 and the total amount is $62?

• 13

• 5

• 11

• 7

What is the cost of one notebook if 7 notebooks cost $5.25?

• $0.75

• $1.25

• $0.50

• $1.00

In the farm problem, if there are 42 animals and 114 legs, how many cows are there?

• 12

• 15

• 27

• 30

What is the area of a rectangle if its length is four times its width and the perimeter is 45 inches?

• 81 square inches

• 72 square inches

• 90 square inches

• 60 square inches

If the sum of angles X and Y is 127° and X is 34° more than half of Y, what is the measure of angle X?

• 62°

• 65°

• 34°

• 93°

What is the main advantage of using linear systems to solve word problems?

• It is easier than drawing diagrams

• It is faster than guessing

• It requires no calculations

• It provides an exact solution

In the exercises, what is the total number of legs if there are 15 cows and 27 chickens?

• 130

• 114

• 120

• 140

What is the measure of angle Y if angle X is 65° and the sum of angles X and Y is 127°?

• 34°

• 93°

• 65°

• 62°