Help with Fraction Problem...

[onesixeight]

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!

[truplayer256]

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

[onesixeight]

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!

[shawoody]

Yeah, I'd like to know too.....

[truplayer256]

6/7 times (X-Y)/8=6(X-Y)/56

Y/4=6(X-Y)/56

Cross multiply

56Y=24X-24Y

[dipla]

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

[onesixeight]

dipla...

Excellent...Thank you very much!