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Learn it your way
A short class with Sarah and her students. The other ways are under More.
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Today, we’re going to learn how to solve word problems using algebra. Can anyone tell me what a word problem is?
Is it a math problem that is written in words instead of numbers?
Exactly! Word problems present a scenario and require us to translate that into a mathematical equation. For example, ‘three times a number plus five equals twenty.’ Can someone express this in equation form?
It would be written as 3x + 5 = 20, right?
Absolutely! In this case, 'x' represents the unknown number we want to find. Now, let’s discuss the steps to isolate x.
To solve the equation 3x + 5 = 20, we need to isolate x. What’s the first step?
I think we need to subtract 5 from both sides to get rid of the 5.
Correct! So, when we subtract 5, what do we have?
We get 3x = 15.
Great! Now, we need to divide both sides by 3. What do we get?
x = 5!
Fantastic! So, the number we were looking for is 5. Remember this process of isolating variables; it’s key for solving word problems.
Now, let’s think about why mastering word problems is important. Can anyone give me a real-life example that could be modeled with a word problem?
Maybe something like calculating the cost of tickets for a concert?
Yes! If a ticket costs $10 and you want to buy several tickets, you can represent the total cost with an equation. For instance, if you want to buy x tickets, the equation would be 10x.
And if I want to spend $100, then it would be 10x = 100?
Exactly! You can solve for x to find out how many tickets you can buy. This kind of setup and calculation is very common in everyday scenarios.
When a word problem comes your way, set it up right and solve today!
Imagine a baker with x cookies, who sold 5. If he has 20 left, how many did he bake in the first place?
W.R.S. - Word-Represents-Solve. First, recognize that it’s a word problem, represent it as an equation, and then solve.
S.I.S.T. - Set Up the equation, Isolate the variable, Solve for the variable, and Thoroughly check your answer.
Term
What is a word problem?
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Term
How do you isolate a variable?
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What is a linear equation?
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A mathematical problem expressed in words, requiring translation into an algebraic expression or equation.
A symbol (often a letter) used to represent an unknown value in mathematical equations.
An equation that makes a straight line when graphed, often in the form ax + b = c.
To manipulate an equation to solve for one variable, typically by getting the variable alone on one side.
This section illustrates how to solve word problems using algebraic equations.
The section focuses on the application of algebraic concepts to solve word problems, specifically focusing on the process of setting up and solving linear equations derived from the problem statement.
In this section, we delve into the strategy of solving word problems using algebraic expressions and equations. Linear equations often represent word problems, enabling us to derive the unknown through systematic steps. Understanding the structure of a word problem helps in translating the words into mathematical statements, thereby allowing algebraic manipulation to find solutions. We explore a practical example: finding a number that satisfies the equation built from a narrative, emphasizing the importance of isolating variables and using inverse operations to achieve the correct answer.