We let x be the amount of money she put in the bank the first year, Then the second year was 2*x, and the third year was 2*2*x=4*x, and the fourth year was 2*2*2*x=8*x.

And the total amount she put in the bank, $450, is the sum of all four years, or $450 = x+(2*x)+(4*x)+(8*x).

This simplifies to $450=15*x.

And therefore, the amount of money she put in the bank the first year was x=$<<30=30>>30.

# Answer

30
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Missy had a giant piggy bank in her bedroom.  Every day she would search the house for change to put in her bank.  After 4 years, the bank was opened and it contained $450 in change.  If the second, third, and fourth-year she doubled the amount of money she put in the bank from the amount she had put in the previous year, how much money, in dollars, did she put in the bank the first year?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
30
Missy had a giant piggy bank in her bedroom.  Every day she would search the house for change to put in her bank.  After 4 years, the bank was opened and it contained $450 in change.  If the second, third, and fourth-year she doubled the amount of money she put in the bank from the amount she had put in the previous year, how much money, in dollars, did she put in the bank the first year?
train