rudy went to the mall to spend some of his money he earned. he spent 1/3 of his money o n a new shirt. He then went to to the music store and bought a cd with 1/3 he had left. At dvds to go he bought a dvd with 1/3 of the money he had left. He stopped once more and bought a book with 1/3 of his remaining. Rudy came home with just $16.00left. how much did he start with?

Let M be the money he earned.

2/3 M is what he has left after new shirt.
2/3*2/3 M is what he has left after cd.
2/3*2/3*2/3M is what he has left after dvd.
16=(2/3)^4 M

M= 16*(3/2)^4=16*81/16=81

check that.

how do you get back from 81/1 to 16/1

16*81/16... the 16/16 divides to 1, leaving 81

what's the final answer??

well youleft out the one third of the money from the book store

To find out how much money Rudy started with, we can work backwards from the amount he had left.

Let's call the amount Rudy started with "x dollars".

He first spent 1/3 of his money on a new shirt, which is (1/3)*x = x/3.
After buying the shirt, he had 2/3 of his money left, which is (2/3)*x = 2x/3.

Next, he went to the music store and bought a CD with 1/3 of the money he had left. This is (1/3)*(2x/3) = 2x/9.
After buying the CD, he had 2/3 of his remaining money left, which is (2/3)*(2x/3) = 4x/9.

Then, he went to DVDs to Go and bought a DVD with 1/3 of the money he had left. This is (1/3)*(4x/9) = 4x/27.
After buying the DVD, he had 2/3 of his remaining money left, which is (2/3)*(4x/9) = 8x/27.

Finally, he bought a book with 1/3 of his remaining money, which is (1/3)*(8x/27) = 8x/81.
After buying the book, he had $16 left, so we can form the equation:

8x/81 + 16 = x

To solve this equation, we can multiply through by 81 to get rid of the fraction:

8x + 1296 = 81x

Next, we can rearrange the equation:

81x - 8x = 1296

73x = 1296

Dividing both sides by 73:

x = 1296/73

Using a calculator, we find that x is approximately 17.73.

Therefore, Rudy started with approximately $17.73.