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