For how many ordered pairs of positive integers (x, y) is x + 2y = 100?

2004 AMC 12A Problem 3

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For how many ordered pairs of positive integers

(x, y)

x + 2y = 100?

33

49

50

99

100

Solve for

x

in terms of

y

x = 100 - 2y

must be positive, which bounds how large the positive integer

y

can be

Writing

x = 100 - 2y,

the value of

x

is a positive integer precisely when

y

is a positive integer with

1 \le y \le 49.

This gives

49

valid ordered pairs.

Thus, the correct answer is B.