Amanda worked hard all summer. Before school started,she decided to go shopping and spend some of her earnings. She spent one third of her money on a new shirt and hot fashions in the mall. He then went to andy's music and brought a CD with one third of the money she had left. At blockbuster she spent one third of the money she had on a DVD that she wanted. She stopped on more time on her way home and brought an iced coffee at dutch bros,with one third of her remaining money. Amanda arrived home with just 16.00$ in her wallet. How much did she have when she started out?

Assume she had $x to spend

after shirt she had (2/3)x left
after CD she had (2/3)(2/3)x left
after DVD she had (2/3)(2/3)(2/3)x left
after iced coffee she had (2/3)(2/3)(2/3)(2/3)x left

(2/3)(2/3)(2/3)(2/3)x = 16
16x/81 = 16
x = 81

To solve this problem, we can work backward and calculate the amount of money Amanda had at each step.

Let's denote the amount of money Amanda had initially as "x."

Step 1: Amanda spent one third of her money on a new shirt and hot fashions. So, she had (2/3)x left.

Step 2: Amanda went to Andy's music and bought a CD with one third of the remaining money. Therefore, she had (2/3) * (2/3)x = (4/9)x left.

Step 3: Amanda went to Blockbuster and spent one third of the remaining money on a DVD. Thus, she had (2/3) * (4/9)x = (8/27)x left.

Step 4: Amanda went to Dutch Bros and bought an iced coffee with one third of the remaining money. She had (2/3) * (8/27) * x = (16/81)x left.

Finally, we know that Amanda arrived home with $16.00, which was equal to (16/81)x. So we can set up the equation:

(16/81)x = $16.00

To solve this equation for x, we can multiply both sides by (81/16):

x = ($16.00 * 81) / 16

x = $81.00

Therefore, Amanda had $81.00 when she started out.