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half that of Chelsea

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by sanju09 » Thu Sep 16, 2010 10:33 pm
Five years ago, Beth's age was three times that of Amy. Ten years ago, Beth's age was one half that of Chelsea. If C represents Chelsea's current age, which of the following represents Amy's current age?
(A) C/6 + 5
(B) 2 C
(C) (C - 10)/3
(D) 3 C - 5
(E) (5/3) C - 10


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by goyalsau » Thu Sep 16, 2010 11:34 pm
I think its A.
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by sanju09 » Thu Sep 16, 2010 11:42 pm
goyalsau wrote:I think its A.
Please share your views along with all of your IMOs.
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by selango » Fri Sep 17, 2010 12:21 am
5 yrs ago
-------------------

B-5=3(A-5)

B-5=3A-15

B=3A-10

10yrs ago
----------------

B-10=1/2(C-10)

2B-20=C-10

2B=C+10

6A-20=C+10

6=C+30

A=C/6+5

Pick A
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by Scott@TargetTestPrep » Sun Jun 02, 2019 4:11 pm
sanju09 wrote:Five years ago, Beth's age was three times that of Amy. Ten years ago, Beth's age was one half that of Chelsea. If C represents Chelsea's current age, which of the following represents Amy's current age?
(A) C/6 + 5
(B) 2 C
(C) (C - 10)/3
(D) 3 C - 5
(E) (5/3) C - 10
Let's let a, b, and c represent the current ages of Amy, Beth, and Chelsea, respectively. We can create the equations:

b - 5 = 3(a - 5)

b - 5 = 3a - 15

b = 3a - 10

and

b - 10 = (1/2)(c - 10)

2b - 20 = c - 10

2b - 10 = c

Substituting, we have:

2(3a - 10) - 10 = c

6a - 20 - 10 = c

6a - 30 = c

a - 5 = c/6

a = c/6 + 5

Answer: A

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