Answer:
Writing an equation to model a real-world problem is often easier when you take the information given in the problem and express it in verbal form by using a few key words. This is very similar to translating verbal phrases into variable expressions. The difference is you will be translating a verbal sentence into an equation. Then, you can solve the equation using inverse operations.
Let’s look at an example.
Monica purchased a pair of tennis shoes that had this sticker on the bottom of the shoe.
$99.00$65.99
Use a verbal model to write and solve an equation to determine the amount of money Monica saved by purchasing the shoes on sale.
First, write a verbal model to represent the problem.
Verbal Model:
Sales Price+Amount Saved=Original Price
Next, name the variable.
Let ‘
s
’ represent the amount saved.
Next, solve the equation you have written. Remember an equation is like a balance scale. To keep the scale balanced, what you do to one side of the equation you must also do to the other side. When solving an equation your goal is to isolate the variable on one side of the equation and the numerical terms on the other side. This is done by performing inverse operations.
65.99+s=99.00
First, isolate the variable ‘
s
’ by subtracting 65.99 from both sides of the equation. Subtraction is the inverse of addition.
65.99−65.99+s=99.00−65.99
Next, simplify each side.
s=33.01
The answer is $33.01.
A variable can be any element that we can, in some way, change.
The general form of modeling and solving real life problems that involve one variable is:
So for example, something that we can define with a variable is "How many of one type of item we can buy if we know its price"
For example, if we know that a shirt costs $10, then the price of x of these shirts is:
y = $10*x
Now, if you know how much money you have, you can use this equation to find how many shirts you can buy.
For example, you know that you have $20, then y = $20
$20 = $10*x
To solve this we need to isolate the variable on one side:
$20/$10 = x
2 = x
You can buy two shirts.
Now, the general form of modeling and solving real life problems that involve one variable is:
If you want to learn more, you can read:
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