Minimum Score on 4th Test for 80 Average in Linear Algebra Course

[Canadian]

This problem is frustrating me, I am a university student taking a course in introductory linear algebra. This problem is on the list of problems we were supposed to do to get used to the computer system, the problems were supposed to be an easy review. The other 9 problems were very simple but this one has me stumped.

Homework Statement

The course you are taking has 4 tests. The first three tests are for 100 points each and the fourth and final test is for 200 points. You must have an average of at least 80 percent on the 4 tests. On the first three tests you scored 74, 84 and 97. What is the minimum score you need on the fourth test to get an 80 for the course?.

The Attempt at a Solution

I think my problem may be with the way I am reading the question?? The way I am interpreting the "points" given for each test. I am interpreting the points as 100 or 200 points out of a total 500, so the first three tests count for 20% of the 80 mark each and the last as 40%.

Here's what I've come up with: X is my variable, the score on the 4th test.

(74*100+84*100+97*100+200X)/500=80
25500+200X=40000
200X=14500
X=72.5

I checked it through my formula and it worked.

(74*100+84*100+97*100+72.5*200)/500=80

Then I thought that the points were in there as a red herring and I simply needed to calculate a simple average and came up with 65% but that answer isn't correct either.

Any help would be appreciated.

 

[EnumaElish]

Could it be a rounding issue? 72.5 = 73?

 

[Canadian]

No I don't think so, on this system if you enter the answer 1/3 as 0.333333333333333333 it will still mark it as correct.

 

[EnumaElish]

If the average is 80 and there are 5 "parts," then sum of the parts = 5*80 = 400.

74 + 84 + 97 + x = 400 ==> x = 145.

 

[Sleek]

A good way to understand this problem would be to see the marks as whole. You need an agg of 80% on the test score. So you need a certain amount of marks out of 500 to get 80 %.

Thus, 74+84+97 is your first test marks.

[(74+84+97+x)/500]*100=80

Solving for x gives 145. So you have to get 145 from the last test out of 200.

 

[Canadian]

Thanks everyone, I was on the right track, but reading it wrong like I thought I may have been.

They were asking for 145/200 not 72.5%.