I'm not sure where I got this problem from, but I have difficulty with these type of fraction problems.
A student took 12 tests. The student's average (arithmetic mean) on the first 4 tests was 6/7 of the student's average on the final 8 tests. What fraction of the total number of points that the student scored on all 12 tests was the total number of points that the student scored on the first 4 tests?
a. 3/20
b. 1/4
c. 3/10
d. 1/3
e. 3/8
Any tips on how to best approach & solve these type of problems?
I tried to set it up as follows:
(sum for first 4 test scores) + (sum of remaining 8 test scores) / 12 = avg of all 12 test scores.
= 6/7x + x / 12 = average of all 12 test scores.
I tried to use a substitution of x=70, but I got 60/130 = 6/13.
Maybe I'm misunderstanding the question stem...
Thanks!
Help with Fraction Problem...
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X= Sum of all the scores on the 12 tests
Y= Sum of all the scores on the 4 tests
Y/4=6/7*(X-Y)/(8)
56Y=24X-24Y
80Y=24X
10Y/3=X
(Y)/(10Y/3)=3/10 C
Y= Sum of all the scores on the 4 tests
Y/4=6/7*(X-Y)/(8)
56Y=24X-24Y
80Y=24X
10Y/3=X
(Y)/(10Y/3)=3/10 C
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I'm almost embarrassed to ask, but how did you get this part:
Y/4=6/7*(X-Y)/(8)
56Y=24X-24Y
Could you explain how 8 got cross multiplied with 7, and 6 and 4 on the other side.
Thanks!
Y/4=6/7*(X-Y)/(8)
56Y=24X-24Y
Could you explain how 8 got cross multiplied with 7, and 6 and 4 on the other side.
Thanks!
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Here is more plausible explanation
Assume first four tests the average is 6
Then last 8 test average is 7 (because first is 6/7 of last 8)
So total 12 tests sum = 8*7 + 6*4 =80
Sum of first 4 tests=4*6 = 24
Ration 24/80=3/10
-Cheers
Assume first four tests the average is 6
Then last 8 test average is 7 (because first is 6/7 of last 8)
So total 12 tests sum = 8*7 + 6*4 =80
Sum of first 4 tests=4*6 = 24
Ration 24/80=3/10
-Cheers
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