Virginia, Adrienne, and Dennis have taught history for a combined tota

Let number of years taught by Virginia = V
number of years taught by Adrienne = A
number of years taught by Dennis = D

V+A+D = 96

V= A+9
=>A = V-9

V= D-9

=> A = (D-9)-9 = D-18

D-9 + D-18 + D = 96
=> 3D = 96 + 27 = 123
=> D = 41

Answer D
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HI All,

This question can be solved by TESTing THE ANSWERS. From the prompt, we know that the three people have taught for a total of 96 years and that Virginia has taught for 9 more years than Adrienne and for 9 fewer years than Dennis. So Dennis taught the HIGHEST number of years (meaning that he had to have taught MORE than 96/3 = 32 years). Looking at the Answers, let's start with D....

Answer D: 41 years

IF....
Dennis = 41 years taught
Virginia = 41 - 9 = 32 years taught
Adrienne = 32 - 9 = 23 years taught
41 + 32 + 23 = 96 years taught

This is an exact match for what the prompt told us, so this MUST be the answer.

Final Answer:

GMAT assassins aren't born, they're made,
Rich
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We can also solve this question using just one variable

Virginia has taught for 9 more years than Adrienne and for 9 fewer years than Dennis
Has both pieces of information are related to Virginia's teaching time, let's let V = the number of years Virginia has taught
This means V - 9 = the number of years Adrienne has taught
And V + 9 = the number of years Dennis has taught

Virginia, Adrienne, and Dennis have taught history for a combined total of 96 years
(Virginia's teaching time) + (Adrienne's teaching time) + (Dennis' teaching time) = 96
Substitute to get: V + (V - 9) + (V + 9) = 96
Simplify: 3V = 96
Solve: V = 32
This means Virginia has taught for 32 years

Since V + 9 = the number of years Dennis has taught, we can substitute to get...
32 + 9 = 41 = the number of years Dennis has taught

Answer: D

Cheers,
Brent
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D.

V + A+ D = 96. ----1
V = A+ 9 or A = V-9
V = D - 9 or D = V + 9

Substituting values for A & D in eq 1

V + V -9 + V + 9 = 96
3V = 96
V = 32

D = 32+ 9 = 41
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Solution:

We can create the following equations:

V + A + D = 96

And

V = A + 9

V - 9 = A

And

V = D - 9

V + 9 = D

Adding the second and third equations, we have:

2V = A + D

Substituting into the first equation, we have:

V + 2V = 96

3V = 96

V = 32

So, D = 32 + 9 = 41.

Answer: D
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V+A+D=96 years

V=D-9 and A=V-9, therefore A=D-18

D-9+D-18+D=96
3D-27=96
3D=123
D=123/3 = 90/3+33/3= 30+11 = 41 years

Alternative approach

V=D-9 so D=V+9
V=A+9 so A=V-9

V+V+9+V-9=96
3V=96
V=96/3= 32 years
D=V+9=32+9=41 years

Answer D)

Virginia, Adrienne, and Dennis have taught history for a combined total of 96 years. If Virginia has taught for 9 more years than Adrienne and for 9 fewer years than Dennis, for how many years has Dennis taught?

(A) 23
(B) 32
(C) 35
(D) 41
(E) 44

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et number of years taught by Virginia = V
number of years taught by Adrienne = A
number of years taught by Dennis = D

V+A+D = 96

V= A+9
=>A = V-9

V= D-9

=> A = (D-9)-9 = D-18

D-9 + D-18 + D = 96
=> 3D = 96 + 27 = 123
=> D = 41