She drinks 1/2 bottle a day and there are 24 bottles in a case so a case will last 24/.5 = <<24/.5=48>>48 days
She needs enough to last her 240 days and 1 case will last her 48 days so she needs 240/48 = <<240/48=5>>5 cases
Each case is on sale for $12.00 and she needs 5 cases so that's 12*5 = $<<12*5=60.00>>60.00
#### 60