Maddy and Lara see a list of numbers written on a blackboard. Maddy adds to each number in the list and finds that the sum of her new numbers is . Lara multiplies each number in the list by and finds that the sum of her new numbers is also . How many numbers are written on the blackboard?
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Problem © Mathematical Association of America (MAA), American Mathematics Competitions. Reproduced for non-commercial educational use. Solution and commentary are original to this site.