Question 1208698: A builder of tract homes reduced the price of a model by 15%. If the new price is $425,000, what was its original price? How much can be saved by purchasing the model?
All throughout my time with math (all my life), setting up the right equation using the given data in word problems has been a major personal frustration.
Here is my effort, which is wrong.
Price of model = x
Reduced by 15% = x - 0.15
Equate to new price:
x - 0.15 = 425,000
This is obviously and miserably wrong.
I know there is a general equation or formula for finding the original price of items. However, let's say you are taking a test and came across this question. You don't know if there is a general equation or formula that can be used to find the original price. How would you approach this problem to find the correct answer?
Found 3 solutions by ikleyn, MathTherapy, greenestamps:
Answer by ikleyn(52754)   (Show Source):
You can put this solution on YOUR website! .
They want you find the ORIGINSAL price.
Let x be the original price.
Reducing the price by 15% means that the reduced price is x - 0.15x, which is 0.85x.
Therefore, the setup equation is
0.85x = 425000 dollars.
From this equation, you easy find the original price
x =  = use your calculator = 500000 dollars.
At this point, the solution is complete.
ANSWER. The original price is $500,000.
CHECK. The reduced price is 500000 - 0.15*500000 = 500000 - 75000 = 425000 dollars. ! correct !
Solved in full, with explanations and checking.
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Answer by MathTherapy(10549)  (Show Source):
You can put this solution on YOUR website!
A builder of tract homes reduced the price of a model by 15%. If the new price is $425,000, what was its original price? How much can be saved by purchasing the model?
All throughout my time with math (all my life), setting up the right equation using the given data in word problems has been a major personal frustration.
Here is my effort, which is wrong.
Price of model = x
Reduced by 15% = x - 0.15
Equate to new price:
x - 0.15 = 425,000
This is obviously and miserably wrong.
I know there is a general equation or formula for finding the original price of items. However, let's say you are taking a test and came across this question. You don't know if there is a general equation or formula that can be used to find the original price. How would you approach this problem to find the correct answer?
You have the right idea, but made a small error, which obviously led to an incorrect EQUATION, which would have
led to an incorrect answer.
Here is my effort, which is wrong.
Price of model = x
Reduced by 15% = x - 0.15 <==== ERROR here! A reduction of 15% on a price of "x" results in a REDUCED PRICE
of x - 15% of x = x - .15x
Equate to new price:
x - 0.15 = 425,000 <==== Equating to NEW REDUCED PRICE will yield the following CORRECT equation:
x - .15x = 425,000.
Answer by greenestamps(13195)  (Show Source):
You can put this solution on YOUR website!
To help you overcome your frustration in setting up equations correctly, it should help to remember that, when things are being combined in an equation using addition or subtraction, the things must be the same kinds of things.
Your equation in this example is
x-0.15=425,000
You have defined x to be the original cost of the model; and 425,000 is the reduced price of the model. So those two things in your equation are the same kinds of things -- they are both prices, or, more generally, amounts of money.
But the 0.15 in your equation is a percentage - it is not an amount of money.
When you are learning to set up equations for solving problem, it might help to be more detailed in what you write -- maybe like this:
original price: x
amount of price reduction: 0.15x ("0.15x" is an amount of money; "0.15" is not)
reduced price: x - 0.15x
reduced price: 425,000
Now you have two expressions for the reduced price. Set those two expressions equal to each other to get the equation you need:
x - 0.15x = 425,000
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