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 Skip Navigation LinksMath Help > Math Puzzles > 2004 State Logic Quiz > Question 04 > Question 04

Academic Decathlon 2004 State Championship Logic Quiz

Question 04

Alice says, "I and Barbara have, together, $76."

Barbara comments, "I and Chloe have $140."

Chloe points out, "If Alice were to give me what she has, then I would have $96."

How much money does each of the girls have?

Answer:

A=16, B=60, C=80.

Translating their statements into algebraic equations,

A+B=76
B+C=140
C+A=96

Adding the three equations,

2A+2B+2C=312
A+B+C=156

Now, subtracting each equation in turn from A+B+C=156, we get the following:

A+B+C=156
A+B   =  76          
C=80

A+B+C=156
    A=16

A+B+C=156
A+   C=  96          
B=60

 

 

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