Answer:
The average verbal reasoning score: 152.4
The average quantitative reasoning score: 153.5
The analytical writing score: 9.2
Step-by-step explanation:
Let's call A the average verbal reasoning score, B the average quantitative reasoning score and C the analytical writing score.
Then, if the average quantitative reasoning score exceeded the average verbal reasoning score by 1.1 points, we can write the following equation:
B = A + 1.1 (eq. 1)
At the same way, if the average verbal reasoning score exceeded the analytical writing score by 143.2 points, we can write the following equation:
A = C + 143.2 or
C = A - 143.2 (eq. 2)
Finally, the sum of the three average scores was 315.1, so:
A + B + C = 315.1 (eq. 3)
Then, replacing equation 1 and 2 in equation 3:
A + B + C = 315.1
A + (A + 1.1) + (A - 143.1) = 315.1
Solving for A:
A + A + 1.1 + A - 143.2 = 315.1
3A = 315.1 - 1.1 + 143.2
3A = 457.2
A = 152.4
Replacing the value of A in equation 1 and 2:
B = A + 1.1 = 152.4 + 1.1 = 153.5
C = A - 143.2 = 152.4 - 143.2 = 9.2
So, the average score for each category is:
The average verbal reasoning score: 152.4
The average quantitative reasoning score: 153.5
The analytical writing score: 9.2