Let's use w to represent the number of weeks.
After w weeks, Ashley will have $100 + $25w.
After w weeks, Vivienne will have $280 - $20w.
We want to find the number of weeks it takes for the two girls to have the same amount of money.
So we can set the two expressions equal to each other and solve for w:
$100 + $25w = $280 - $20w
$45w = $180
w = 4
Therefore, it will take 4 weeks for Ashley and Vivienne to have the same amount of money.