Apatient needs to be given exactly 1000 ml of a 5.0% (w/v) intravenous glucose solution. the stock solution is 55% (w/v). how many milliliters of the stock solution are needed to prepare the fluid for the iv bag?

The patient needs 1000 ml of 5% (w/v) glucose solution
i.e  1000 ml x 5 g/ 100 ml 
where the stock solution is 55% (w/v) = 55 g / 100 ml  
So, 1000 ml x 5 g / 100 ml = V (ml) x 55 g / 100 ml 
V = 1000 x (5 / 100) / (55 / 100) = 5000 / 55 = 90.9 ml 
∴ the patient needs 90.9 ml of 55% (w/v) glucose solution