How do you solve word problems by solving equations?

For example, let’s say you’re trying to decide on a cell phone plan. Plan 1 is

$30 plus $0.01 per text and plan 2 is $5 plus $0.10 per text. How many texts

would you need to use for the plans to cost the same?

In this lesson you will learn how to solve word problems by

solving equations with one variable.

Let’s Review4x - 15 = 9 - 2x

x #

+15 +154x = 24 - 2x+2x +2x6x = 24

x = 44(4) - 15 = 9 - 2(4)

x  16 x  16

Core Lesson

Cost A = Cost B40 + 4x = 100 + 2x

Your school is planning a field trip to a zoo. There are two different bus companies that the school can use. The school wants to know how many students will need to go in order for the two companies to cost the same. Bus A costs a $40 rental fee, plus $4 for each student. Bus B costs a $100 rental fee, plus $2 for each student.

Core Lesson40 + 4x = 100 + 2x

x #

-40 -40

4x = 60 +2x-2x -2x2x = 60

x = 30 students

40 + 4(30) = 100 + 2(30)

x  12 x  12

A Common Mistake

Not checking your answer to make sure it is logical.

In this lesson you have learned how to solve word problems by solving one-variable equations.

Guided PracticeYou get a summer job with a company mowing lawns. They offer you two different deals. You want to know how many lawns you need to mow in order for them to pay the same throughout the whole summer. Company A offers you $55 at the beginning and then $8 for each lawn that you mow. Company B offers you $23 and then $12 for each lawn that you mow.

Guided Practice55 + 8x = 21 + 12x

Extension Activities

Write your own word problem using the following equation. Make sure that your word problem makes sense logically. Solve the equation. Explain what your answer means in terms of your word problem.

3x + 19 = 42 - 2x

Extension Activities

Write your own word problem and write an equation that represents your problem. Make sure your problem and answer make sense. Explain the meaning of all of the numbers (including your solution) in terms of your word problem.

Quick Quiz

You want to become a member of a website that allows you to download a certain number of MP3s for a price. There are two different options. Option A costs $6 a month, plus $0.50 per MP3 downloaded. Option B costs $12 a month and only $0.10 per MP3 downloaded. How many MP3s do you need to download for the two options to cost the same?

It cost $284 for a class to go on a field trip. The bus cost $140 and then the museum cost $3 per student. Write and solve an equation to find out how many students went on the field trip.