If for any three distinct numbers a, b, and c we define a,b,c=(c+a)/(c-b), then 1,-2,-3=

1991 AMC 12 Problem 1

Attempt Problem 1 of the 1991 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1991 AMC 12 solutions, or check the answer key.

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If for any three distinct numbers

a,

b,

and

c

we define

\boxed{a,b,c}=\frac{c+a}{c-b},

then

\boxed{1,-2,-3}=

-2

-\frac25

-\frac14

\frac25

2

Substitute

a=1,

b=-2,

and

c=-3

into the definition

Be careful with the two negative signs in the denominator

Direct substitution gives

\begin{aligned} \boxed{1,-2,-3} &=\frac{-3+1}{-3-(-2)}\\ &=\frac{-2}{-1}=2. \end{aligned}

Thus the correct answer is E.