SOLUTION: A student has four exams scores. The average of the first two scores is 50. The average of the second and third is 75 and the average of the third and fourth is 70. What is the ave

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Question 699445: A student has four exams scores. The average of the first two scores is 50. The average of the second and third is 75 and the average of the third and fourth is 70. What is the average of the first and fourth scores?
a)45
b)50
c)90
d)100
e)None of the above
Answer by DrBeeee(684) About Me  (Show Source):
You can put this solution on YOUR website!
We have three equations based on the average of two scores is one-half the sum of the two scores, or the sum is twice the average.
(1) S1 + S2 = 2*50
(2) S2 + S3 = 2*75
(3) S3 + S4 = 2*70
Now to solve, first substitute S2 of (2) into (1) and get
(4) S1 + (150 - S3) = 100 or
(5) S1 = S3 -50
Now substitute S3 of (3) into (5) and get
(6) S1 = (140 - S4) - 50 or
(7) S1 + S4 = 90 giving us the average of S1 and S4
(8) (S1+S4)/2 = 90/2 or 45
The answer is choice a)