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Learn how to build and solve linear equations from word problems step by step with a focus on identifying variables, constants, rates of change, and the end result.
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Building Linear Equations from Word Problems
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 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.
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
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.
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).
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.
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 perminute. 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.
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 perminute. How many minutes, m, will it take for the two containers to have the same amount of water? Container A = Container B m + 800 = m + 1000 Since each container started with a specified amount you will add the 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 perminute. 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.)
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 perminute. How many minutes, m, will it take for the two containers to have the same amount of water? − 6 ● m + 800 = −10 ● m + 1000 Multiply the rate of change by the variable(s). Since you are leaking the rate of change is negative.
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 perminute. How many minutes, m, will it take for the two containers to have the same amount of water? −6m + 800 = −10m + 1000 Or 800 − 6m = 1000 − 10m You have built an equation!! And you are ready to solve
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?
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?
