Difference between revisions of "2023 AMC 10B Problems/Problem 5"
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From the second equation, <math>S=15</math>, so <math>15+3x=45</math>. Solving, we find <math>x=\boxed{\textbf{(E) }10}.</math> | From the second equation, <math>S=15</math>, so <math>15+3x=45</math>. Solving, we find <math>x=\boxed{\textbf{(E) }10}.</math> | ||
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~Mintylemon66 | ~Mintylemon66 |
Revision as of 16:03, 15 November 2023
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