Question 1133195: Walmart has a bike on sale for $150. The sign next to it says that the price is $25 off the original price. What is the original price? Define the variable and equation for the situation. Solve the equation.
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This question is from my son's Math test. His answer is as follows:
Let x = original price
x = 150 + 25; x = 175.
His teacher marked it wrong and wrote the equation as x - 25 = 150.
I don't see how the equation my son wrote is wrong? Could you please help me understand?
Found 4 solutions by Boreal, math_helper, Alan3354, MathTherapy:
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! Basically, he did it fine, but I think the teacher may have wanted him to set up the variable and take $25 off it.
x=the original price
25 off the original price is x-25
That is equal to $150
so x-25=$150, and x+$150+$25, or $175.
I would at least give partial credit.
The purpose of this type of problem is to make students define the variable and set up the equation for more complex problems.
If the bicycle is on sale for $150, and it is 25% off the original price, what was the original price? One can do that in one's head, perhaps, but it is much easier to make a mistake.
x=orignal price, so 0.75x-sale price. The sale price is $200, so 0.75x=$150, x=$200. That is a lot easier (faster and safer, too) than guessing and checking.
A lot of word problems can be dealt with in many ways. If there is a problem about 25% off, that can mean 75% of the original OR, one can calculate the 25% off and subtract it from the original amount. Both of those ways are acceptable.
Sometimes, it is easier to do one way than the other. Alex is 4 years less than twice as old as Bob. Here, Bob is the youngest, so let his age be x, not Alex's age, where Bob will be some fractional amount of age. If Bob is x then Alex is 2x-4, which is 4 fewer than twice as much.
Answer by math_helper(2461)  (Show Source):
You can put this solution on YOUR website! x = 150 + 25 is equivalent to x - 25 = 150 (just add 25 to both sides to see this)
I think his teacher is expecting to see the "proper" starting formulation of
x - 25 = 150, which indeed makes a little more sense from the problem description.
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As an example, consider this simple age problem:
John is 6 years younger than Alan
Alan's age and John's age add to 70
Find Alan's age
Let Alan's age be x
John's age is then: x - 6
As a teacher, I would expect the starting formulation to be:
(x) + (x-6) = 70
One wouldn't expect the student, instead, to create a starting formulation of:
2x = 76
even though they are equivalent.
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Just to follow up: I used "proper" loosely to mean "most representative of the problem described." As tutor Boreal said, it is easy to make a mistake if one starts solving the problem in their head.
You know the starting point should be x-25=150 because the problem asks for the original price and it says "$25 off the original" (off ==> subtraction).
Basically your son partly solved the equation "x-25=150" in his head to arrive at the equivalent "x=150+25" which will be error-prone for more complex problems.
Answer by Alan3354(69443)  (Show Source):
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website! Walmart has a bike on sale for $150. The sign next to it says that the price is $25 off the original price. What is the original price? Define the variable and equation for the situation. Solve the equation.
_______________________________________________________________________
This question is from my son's Math test. His answer is as follows:
Let x = original price
x = 150 + 25; x = 175.
His teacher marked it wrong and wrote the equation as x - 25 = 150.
I don't see how the equation my son wrote is wrong? Could you please help me understand?
I guess he didn't write the correct equation based on the way the problem was formulated.
Let original price be x
Price after $25 discount: x - 25
Also, it was given that the price after discount or sale price = 150
We then EQUATE them to get: x - 25 = 150
That's somewhat PETTY though. I agree with the other tutor that partial credit should have been awarded, because if this problem were on an exam,
whether open-ended or multiple choice, he would've gotten FULL MARKS.
I guess though that this must be a lesson on following EXACT INSTRUCTIONS and the way he wrote it was not EXACTLY how itw's stated.
A good lesson, I guess for someone young showing he/she how important it is to follow INSTRUCTIONS precisely.
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