1. Building Linear Equations
from Word Problems

2. What to do in the equation
Step
Things to remember
What to do in the equation
Step 1:
Step 2:
Step 3:
Step 4:

3. Container A and Container B have leaks
Container A and Container B have leaks. Container A has 800 ml of water, and is leaking 6ml per minute. Container B has 1000 ml of water, and is leaking 10 ml per minute. How many minutes, m, will it take for the two containers to have the same amount of water?

4. Step 1: Identify the variables
Container A and Container B have leaks. Container A has 800 ml of water, and is leaking 6ml per minute. Container B has 1000 ml of water, and is leaking 10 ml per minute. How many minutes, m, will it take for the two containers to have the same amount of water?
Step 1: Identify the variables
Variables represent values that can change.
There may be one, two or several in a word problem.

5. Container A and Container B have leaks
Container A and Container B have leaks. Container A has 800 ml of water, and is leaking 6ml per minute. Container B has 1000 ml of water, and is leaking 10 ml per minute. How many minutes, m, will it take for the two containers to have the same amount of water?
m m
Write letters for the variables that will help you remember what they represent. Sometimes they tell you which variable to use

6. Container A and Container B have leaks
Container A and Container B have leaks. Container A has 800 ml of water, and is leaking 6ml per minute. Container B has 1000 ml of water, and is leaking 10 ml per minute. How many minutes, m, will it take for the two containers to have the same amount of water?
Notice that this problem asks for when the containers have the same amount and only refers to one variable. That is a clue that the equation will have variables on both sides of the equal sign.

7. Step 2: Identify the end result of the situation.
Container A and Container B have leaks. Container A has 800 ml of water, and is leaking 6ml per minute. Container B has 1000 ml of water, and is leaking 10 ml per minute. How many minutes, m, will it take for the two containers to have the same amount of water?
Step 2: Identify the end result of the situation.
This may be a variable (if you don’t know the value) or a number (if the value is given).

8. Container A and Container B have leaks
Container A and Container B have leaks. Container A has 800 ml of water, and is leaking 6ml per minute. Container B has 1000 ml of water, and is leaking 10 ml per minute. How many minutes, m, will it take for the two containers to have the same amount of water?
m = m
Put the end result after the equal sign. In this case we are having a variable equal to itself because the end results is minutes.

9. Step 3: Identify any constants.
Container A and Container B have leaks. Container A has 800 ml of water, and is leaking 6ml per minute. Container B has 1000 ml of water, and is leaking 10 ml per minute. How many minutes, m, will it take for the two containers to have the same amount of water?
Step 3: Identify any constants.
A constant is a value that will stay the same no matter what the variables are.
Figure out if the constant is being added or subtracted.

10. Container A = Container B m + 800 = m + 1000
Container A and Container B have leaks. Container A has 800 ml of water, and is leaking 6ml per minute. Container B has 1000 ml of water, and is leaking 10 ml per minute. How many minutes, m, will it take for the two containers to have the same amount of water?
Container A = Container B
m = m
Since each container started with a specified amount you will add the constants.

11. Step 4: Identify the rate(s) of change.
Container A and Container B have leaks. Container A has 800 ml of water, and is leaking 6ml per minute. Container B has 1000 ml of water, and is leaking 10 ml per minute. How many minutes, m, will it take for the two containers to have the same amount of water?
Step 4: Identify the rate(s) of change.
The rate of change is how much the total will change each time the variable changes.
In a linear equation, the rate of change will remain steady.
Since this has a variable on each side of the equal sign there will be two rates. (per is a good clue of what the rate will be.)

12. Container A and Container B have leaks
Container A and Container B have leaks. Container A has 800 ml of water, and is leaking 6ml per minute. Container B has 1000 ml of water, and is leaking 10 ml per minute. How many minutes, m, will it take for the two containers to have the same amount of water?
− 6 ● m = −10 ● m
Multiply the rate of change by the variable(s). Since you are leaking the rate of change is negative.

13. Container A and Container B have leaks
Container A and Container B have leaks. Container A has 800 ml of water, and is leaking 6ml per minute. Container B has 1000 ml of water, and is leaking 10 ml per minute. How many minutes, m, will it take for the two containers to have the same amount of water?
−6m = −10m Or
800 − 6m = 1000 − 10m
You have built an equation!!
And you are ready to solve

14. Next problem: Tim is choosing between two cell phone plans that offer the same amount of free minutes. Dingaling’s plan charges $39.99 per month with additional minutes costing $0.45. Belltone’s plan cost $44.99 with additional minutes at $0.40. How many additional minutes, a, will it take for the two plans to cost the same?

15. Another problem: The cost to purchase a song from iTunes is $0
Another problem: The cost to purchase a song from iTunes is $0.99 per song. To purchase a song from Napster, you must be a member. The Napster membership fee is $10. In addition, each purchased song costs $0.89. How many downloaded songs, d, must be purchased for the monthly price of Napster to be the same as iTunes?

16. What to do in the equation
Step
Things to remember
What to do in the equation
Step 1: Identify the variables
Variables represent values that can change.
There may be one, two or several in a word problem.
Write letters for the variables that will help you remember what they represent
Step 2: Identify the end result of the situation.
The end result may be a variable (if you don’t know the value) or a number (if the value is given).
Put the end result after the equal sign.
Step 3: Identify any constants.
A constant is a value that will stay the same no matter what the variables are.
Figure out if the constant is being added to or subtracted from the total.
Add or subtract the constant(s).
Step 4: Identify the rate(s) of change.
The rate of change is how much the total will change each time the variable changes.
In a linear equation, the rate of change will remain steady.
Multiply the rate of change by the variable(s).