2024 AMC 8 Problems/Problem 8
Problem
On Monday Taye has $2. Every day, he either gains $3 or doubles the amount of money he had on the previous day. How many different dollar amounts could Taye have on Thursday, 3 days later?
==Solution 1== (BRUTE FORCE)
How many values could be on the first day? Only dollars. The second day, you can either add
dollars, or double, so you can have
dollars, or
. For each of these values, you have
values for each. For
dollars, you have
dollars or
, and for
dollars, you have
dollars or
. Now, you have
values for each of these. For
dollars, you have
dollars or
, for
dollars, you have
dollars or
8
16
11
7
14
10
{$11}$ (Error compiling LaTeX. Unknown error_msg),${$ (Error compiling LaTeX. Unknown error_msg)16}
8-2 = \boxed{(C) 6}$ different values