1959 AMC 12 Problem 17

Attempt Problem 17 of the 1959 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 1959 AMC 12 solutions, or check the answer key.

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17.

y=a+\dfrac bx,

where

a

and

b

are constants, and if

y=1

when

x=-1,

and

y=5

when

x=-5,

then

a+b

equals:

-1

0

1

10

11

Substitute the two given input-output pairs

Solve

a-b=1

and

a-\frac{b}{5}=5

The two conditions give

a-b=1,\qquad a-\frac b5=5.

Subtracting yields

\frac{4b}{5}=4,

b=5

and

a=6.

Therefore

a+b=11.

Thus, the correct answer is E.

Problem 17 in other years