Math Lesson 9.2.4 - Solving Word Problems through Equations

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Welcome to our Math lesson on Solving Word Problems through Equations, this is the fourth lesson of our suite of math lessons covering the topic of Word Problems Involving Equations, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.

Word Problems that are better to solve only through Equations

There are some word problems that are only solved through equations, as otherwise, it would take too long to solve them step by step. Let's consider a couple of examples to clarify this point.

Example 4

The sum of three consecutive odd numbers is 39. What are the numbers?

Solution 4

We can express the smallest of the numbers by x. Hence, since the odd numbers increase by 2 in respect to the previous ones, the next number is x + 2 and the other is x + 4. Therefore, the equation obtained in this problem is

x + (x + 2) + (x + 4) = 39
x + x + 2 + x + 4 = 39
3x + 6 = 39
3x + 6 - 39 = 39 - 39
3x - 33 = 0

This is the regular form of a first - order equation with one variable where a = 3 and b = -33. Thus, the smallest number is

x = - b/a
= - -33/3
= 33/3
= 11

The next number therefore is 11 + 2 = 13 and the biggest number is 11 + 4 = 15.

Another example:

Example 5

I think of a number. I multiply it by 8 and then subtract 7. The result equals -3. What number was I thinking of?

Solution 5

Let's express the unknown number by x. Multiplying it by 8 means 8x. Thus, the equation derived from the clues of this problem is

8x - 7 = - 3
8x - 7 + 3 = - 3 + 3
8x - 4 = 0

This is the regular form of a first - order equation with one variable where 8 = 3 and b = -4. The value of the variable x therefore is

x = - b/a
= - -4/8
= 4/8
= 1/2

Equations Learning Material
Tutorial ID	Math Tutorial Title	Tutorial	Video Tutorial
9.2	Word Problems Involving Equations
Lesson ID	Math Lesson Title	Lesson	Video Lesson
9.2.1	One-Step Problems Using First-Order Equations
9.2.2	Two-Steps Problems Using First-Order Equations
9.2.3	Solving Problems that Involve More than Two Steps
9.2.4	Solving Word Problems through Equations
9.2.5	Equations for solving Word Problems
9.2.6	Creating Word Problems from Equations

Whats next?

Enjoy the "Solving Word Problems through Equations" math lesson? People who liked the "Word Problems Involving Equations lesson found the following resources useful:

Word Equations Feedback. Helps other - Leave a rating for this word equations (see below)
Equations Math tutorial: Word Problems Involving Equations. Read the Word Problems Involving Equations math tutorial and build your math knowledge of Equations
Equations Video tutorial: Word Problems Involving Equations. Watch or listen to the Word Problems Involving Equations video tutorial, a useful way to help you revise when travelling to and from school/college
Equations Revision Notes: Word Problems Involving Equations. Print the notes so you can revise the key points covered in the math tutorial for Word Problems Involving Equations
Equations Practice Questions: Word Problems Involving Equations. Test and improve your knowledge of Word Problems Involving Equations with example questins and answers
Check your calculations for Equations questions with our excellent Equations calculators which contain full equations and calculations clearly displayed line by line. See the Equations Calculators by iCalculator™ below.
Continuing learning equations - read our next math tutorial: Identities

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