SOLUTION: Ted knows about a marble machine that doubles the number of marbles you put in and adds 24 marbles. One day he put in a certain number and got back a new number. He put the new nu

Question 562230: Ted knows about a marble machine that doubles the number of marbles you put in and adds 24 marbles. One day he put in a certain number and got back a new number. He put the new number in the machine and got back 360 marbles. How many marbles did he put in the machine in the first place

Answer by issacodegard(60) (Show Source): You can put this solution on YOUR website!
Hi, let's denote the effect of the marble machine by the function,
f(n)=2n+24
Where we input n marbles and output 2n+24 marbles.
One day x marbles were input and thus f(x) marbles were output. Then f(x) was input and thus output was f(f(x)) marbles, but as written in the problem was 360 marbles.
So we solve f(f(x))=360 for x
Therefore, we have
f(f(x))=f(2x+24)=2(2x+24)+24=4x+72=360
So, x=72, which was the original number of marbles input.
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