Solve the problem

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 analytical writing score. In​ 2013, the average quantitative reasoning score exceeded the average verbal reasoning score by 1.8 ​points, and the average verbal reasoning score exceeded the analytical writing score by 147.9 points. The sum of the three average scores was 318.3. What was the average score for each​ category?

The average verbal reasoning score was

______.

​(Type an integer or a​ decimal.)

Answer 1

To solve this problem, you have to form a system Equations:

Let Vr = average verbal reasoning score

qr = average qualitative reasoning score

Aw = Average analytical writing score

From the problem statement:

Vr = Aw + 147.9 ... eq 1, qr = Vr + 1.8 eq ...2 , and Vr + qr + Aw = 318.3 ...eq 3

Substitute eq 1 in eq 3 , Vr + ( Aw + 1.8) + Aw = 318.3, Vr + 2 Aw + 1.8 = 318.3, and

Vr + 2 Aw = 318.3 - 1.8 = 316.5 , Vr + 2 Aw = 316.5 ...eq 4

put eq 1 and eq 4 together:

Vr = Aw + 147.9 ... eq 1

Vr + 2 Aw = 316.5 ...eq 4 you have two equations two unknowns Vr and Aw

Substitute eq 1 in eq 4 then ( Aw + 147.9) + 2 Aw = 316.5 ...eq 5 has one unknown Aw solve

3 Aw + 147.9 = 316.5 , 3 Aw = 316.5 - 147.9 = 20.7 , and Aw = 6.9

Substitute the value of Aw on eq 1 , Vr = 6.9 + 147.9 = 154.8

Substitute the value of Vr in eq.2 , qr = 154.8 + 1.8 = 156.6

Check: Vr + qr + Aw = 154.8+156.6+6.9= 318.3 checks

Answer:

The average verbal reasoning score is Vr= 154.8

Answer 2

w represents the writing score

w + 147.9 represents the verbal score

w + 147.9 + 1.8 represents the quantitative score

w + w + 147.9 + w + 147.9 + 1.8 = 318.3

Can you solve for w and answer?