Answer: the youngest sister gets $30
Explanation:
Let x represent the amount of money that the youngest sister gets.
If the middle sister gets twice as much as the youngest sister, it means that the amount of money that the middle sister gets is 2x
If the oldest sister gets three times as much as the youngest sister, it means that the amount of money that the oldest sister gets is 3x
If the total amount of money that they received is $180, it means that
x + 2x + 3x = 180
6x = 180
x = 180/6
x = $30