Virginia, Adrienne, and Dennis have taught history for a combined total of 96 years. If Virginia has taught...

[BTGmoderatorLU]

Source: GMAT Prep

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

The OA is D

[Brent@GMATPrepNow]

Source: GMAT Prep

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

The OA is D

We can 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

[Scott@TargetTestPrep]

Source: GMAT Prep

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

The OA is D

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