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