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

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Virginia, Adrienne, and Dennis have taught history for a combined tota  [#permalink]

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New post 24 Nov 2015, 09:46
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A
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C
D
E

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  15% (low)

Question Stats:

80% (01:41) correct 20% (01:45) wrong based on 65 sessions

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Re: Virginia, Adrienne, and Dennis have taught history for a combined tota  [#permalink]

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New post 24 Nov 2015, 10:04
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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Re: Virginia, Adrienne, and Dennis have taught history for a combined tota  [#permalink]

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New post 24 Nov 2015, 23:36
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.

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Re: Virginia, Adrienne, and Dennis have taught history for a combined tota  [#permalink]

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New post 24 May 2020, 07:59
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Bunuel wrote:
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
PS21154


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

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Re: Virginia, Adrienne, and Dennis have taught history for a combined tota  [#permalink]

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New post 24 May 2020, 14:04
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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Re: Virginia, Adrienne, and Dennis have taught history for a combined tota  [#permalink]

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New post 05 Jun 2020, 10:47
Bunuel wrote:
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


PS21154


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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Re: Virginia, Adrienne, and Dennis have taught history for a combined tota   [#permalink] 05 Jun 2020, 10:47

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

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