2023 AMC 10B Problems/Problem 5
Problem
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?
Solution
Let there be numbers in the list of numbers, and let their sum be
. Then we have the following
From the second equation, , so
. Solving, we find
~Mintylemon66