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Bunuel
Alice is twice as old as Brian and Cathy is 6 years younger than Brian. If Alice is a years old, how old is Cathy in terms of a ?

A. a + 6
B. a − 6
C. (a - 12)/2
D. (a + 12)/2
E. 2a − 6

GIVEN: Alice is a years old

Alice is twice as old as Brian
This also means Brian is HALF as old as Alice
So, Brian's age = a/2

Cathy is 6 years younger than Brian
So, Cathy's age = (Brian's age) - 6
So, Cathy's age = (a/2) - 6

How old is Cathy in terms of a ?
Cathy's age = (a/2) - 6
= a/2 - 12/2
= (a - 12)/2

Answer: C

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Bunuel
Alice is twice as old as Brian and Cathy is 6 years younger than Brian. If Alice is a years old, how old is Cathy in terms of a ?

A. a + 6
B. a − 6
C. (a - 12)/2
D. (a + 12)/2
E. 2a − 6

Break down and solve
Quote:
Alice is twice as old as Brian
a = 2b
Quote:
Cathy is 6 years younger than Brian.
c = b - 6

So, We can say : \(c = \frac{a}{2} - 6\) ie, \(\frac{(a - 12)}{2}\)

Answer must be (C)
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a = 2b ==> b = a/2
c = b-6 ==> c = (a/2) - 6 ==> c = (a-12) / 2 ---- ANSWER = C
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Bunuel
Alice is twice as old as Brian and Cathy is 6 years younger than Brian. If Alice is a years old, how old is Cathy in terms of a ?

A. a + 6
B. a − 6
C. (a - 12)/2
D. (a + 12)/2
E. 2a − 6


We are given that a = Alice’s current age, and we can let b = Brian’s current age and c = Cathy’s current age and create the equations:

a = 2b

and

c = b - 6

c + 6 = b

Substituting, we have:

a = 2(c + 6)

a = 2c + 12

a - 12 = 2c

(a - 12)/2 = c

Answer: C
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Make B=X, so
A=2X
C=X-6

Make a=2X, so X=a/2.

C=(a/2)-6 = (a-12)/2

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