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 variableVirginia has taught for 9 more years than Adrienne and for 9 fewer years than DennisHas 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 =
32This 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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