Caged counting

Algebra Level 1

While caged up by the evil witch, Hansel and Gretel decide to count numbers to pass the time. Hansel starts from the number 502 and counts forward by 2's. Gretel starts from the number 999 and counts backward by 5's. If they both start at the same time, and count at the same rate, what number will they say at the same time?

Details and assumptions

Hansel counts off \( 502, 504, 506, \ldots \)
Gretel counts off \( 999, 994, 989, \ldots \)


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