SOLUTION: I think I have the right answer, but I can't remember how to "show" the work / explain how I got the answer! You get a mark of 80% on the first test, and the average of the m

Question 718456: I think I have the right answer, but I can't remember how to "show" the work / explain how I got the answer!
You get a mark of 80% on the first test, and the average of the marks of the first two tests is 15% higher than the mark on the last one. The average of all marks is 70%. What are the marks of all three tests.
By looking at the question, it appears that the first two test marks are 80 + 70 = 150 /2 = 75%
Therefore, the remaining mark is 60%, which is 15% less than the average of the first two.
(and 80 + 70 + 60) = 70% average / 210 total percent over 3 tests.
However, I just managed to get the answer from this simple question by "looking" at it.
Would somebody please teach me how to "properly" solve it so that I can understand & solve more complicated variations in the future?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
You get a mark of 80% on the first test, and the average of the marks of the first two tests is 15% higher than the mark on the last one.
The average of all marks is 70%. What are the marks of all three tests.
:
Looking at your answer, I noticed that 75 is not 15% more than 60, anyway
:
Let x = the mark on the third test
then
"the average of the marks of the first two tests is 15% higher than the mark on the last one"
2(1.15x) = total marks on the 1st two tests
:
= 70
2.30x + x = 3(70)
3.30x = 210
x = 210/3.3
x = 63.64, his grade on the third test
:
Then
1.15(63.64) = 73.18 is the average on the 1st two test
:
Find the mark on the 2nd test, call it y:
= 73.18
80+y = 2(73.18)
y = 146.36 - 80
y = 66.36 is the grade on the 2nd test
:
What are the marks of all three tests. 80, 66.36, 63.64
:
See if this works out
av =
av = = 70
and find 15% more than the 3rd grade
1.15(63.64) = 73.2 which is the average of 80 and 66.36

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