Question

Many graduate schools require applicants to take a certain test. Those taking the test receive three scores: a verbal reasoning score, a quantitative reasoning score, and an analyticalwriting score. In 2013, the average quantitative reasoning score exceeded the average vorbal reasoning score by 1.4 points, and the average verbal reasoning score exceeded theanalytical writing score by 141.5 points. The sum of the three average scores was 314.4. What was the average score for each category?The average verbal reasoning score was(Type an integer or a decimal)

Answer 1

As given by the question,

There are given that three test score, verbal reasoning score, quantitaive reasoning score and an analytical writing score.

Now,

Let v is the averahe verbal reasoning score, q is the average qualitative reasoning score, and A is the average analytical writing score.

Then,

From the given problem statement

Suppose analytical reasoning score is x

Then,

The verbal reasoning score is:

$\text{verbal}=x+141.5$

And,

The quantitative reasoning score is:

$\text{quantitative}=x+141.5+1.4$

Now,

The sum of the three average scores was 314.4

S,

$\begin{gathered} x+x+141.5+x+141.5+1.4=314.4 \\ 3x+284.4=314.4 \\ 3x=314.4-284.4 \\ 3x=30 \\ x=10 \end{gathered}$

x=10, this is the analytical score.

Then,

For the verbal score, put x=10 into the equation of verbal

So,

$\begin{gathered} \text{verbal}=x+141.5 \\ \text{verbal}=10+141.5 \\ \text{verbal}=151.5 \end{gathered}$

And,

The quantitative score is,

Put the value of x into the equation of quantitative

So,

$\begin{gathered} \text{quantitative}=x+141.5+1.4 \\ \text{quantitative}=10+141.5+1.4 \\ \text{quantitative}=152.9 \end{gathered}$

Hence, the average score of analytical is 10, the average score of verbal is 151.5 and the average score of quantitative is 152.9.