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Virginia, Adrienne, and Dennis have taught history for a com
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09 Jun 2020, 09:14
09 Jun 2020, 09:14
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Question Stats:
65% (01:20) correct
35% (02:10) wrong based on 40 sessions
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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
(A) 23
(B) 32
(C) 35
(D) 41
(E) 44
Re: Virginia, Adrienne, and Dennis have taught history for a com
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09 Jun 2020, 09:14
09 Jun 2020, 09:14
Expert Reply
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Re: Virginia, Adrienne, and Dennis have taught history for a com
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09 Jun 2020, 09:46
09 Jun 2020, 09:46
Carcass 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
(A) 23
(B) 32
(C) 35
(D) 41
(E) 44
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
