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.
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?
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
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.