Two pieces of information are missing:
1) What did the teacher mean? *1.1 or +0.10?
2) What score was given on the exam? Does she get 10% for failing?
No need to dispute entirely ambiguous circumstances.
Hello,
Someone and I have gotten into a dispute over the wording of a word problem. Here is the problem:
Jane currently has a C+ (77%) in her math class. If she does a make-up test her teacher is willing to increase her final grade by 10%. What will Jane's final grade be if she does the test?
Now, before I tell you what I think the answer is and what my friend thinks the answer is, I want your guys' opinions on this.
What is the correct equation to solve this problem?
Thanks,
hapsburg
1) This is what I'm trying to discern. Now, my opponent says it's 1.1, which I agree with. But the teacher says that it's + 0.10. Ambigious, yes. But I can see where she derives this formula from. Logically following through results in x + 0.1 = y, but most people would claim that you have to use x + 0.1*x = y. What I am trying to figure out is if you can formulate the equation that my teacher claims is correct from the word problem. Apparently, you can. My opponent claims there is no possible way you could ever add 0.1 to the grade for whatever reason. I see that both the final grade and 0.1 are percentages and can therefore be added together.
My question boils down to this:
From the ambigious problem, can:
x + .1 = y
be derived from the information given, or is the only possible equation that can be derived is:
x + .1x = y
?
As I see it, there is one equation which will solve all problems here:
m(e + i) = y
where:
m = Maximum amount/Current amount (depending on the wording)
e = The percentage of m earned
i = The percentage of increase or decrease
y = The new amount
To decide between whether or not to use the maximum or the current amount, we must look at the problem:
"increase her grade by 10%"
Since the 10% is not limited by "her grade", we can assume that the maximum amount that can be earned is 100% (the typical grading scale). The equation could be calculated with m = "her final grade amount" but that is not specifically stated within the question. Why assume information about the problem when you have a problem which is possible to solve with a value for x? On the other hand, if the quesiton was:
"increase her grade by 10% of her final grade"
then yes, the only equation you could use is where m = "her final grade" because it is specifically stated in the question.
Honestly, to arrive at my equation, you should use:
"increase her grade by 10% of the total grade"
but I see no reason why you can't assume this information any less legitimately than assuming "of her final grade" is what we are adding 10% of. Is this reasonable?
I arrived at this conclusion because of how 10% of her final grade is derived:
x + x*.1 = y
which can be rewritten as x(1 + .1) = y.
Because the literally (and please tell me if I have translated this incorrectly) translated equation becomes:
x + .1 = y
Where x is a fraction (because it is a grade), you cannot take an x out. You can take any other number, which would allow this to be applied to ANY grading scale.
Now, unless I have made some siginificant error in algebraic analysis, I see no reason why I cannot use this equation. If you see anything wrong with my analysis, please tell me.
2) I didn't word this entirely correctly when I went back and looked at it.
The "test" is really more of a boolean: "Did you do this or didn't you?" and is not factored into final grade.