Final answer:
To determine the resultant percentage strength, we need to calculate the amount of tretinoin added to the gel and then divide it by the total mass of the resultant mixture. The resultant percentage strength is approximately 0.249%.
Step-by-step explanation:
To determine the resultant percentage strength, we need to calculate the amount of tretinoin added to the gel and then divide it by the total mass of the resultant mixture.
First, we need to convert the concentration of the gel from w/w to milligrams per gram (mg/g). The concentration of the 0.4%w/w gel is 0.4g/100g, which is equal to 4mg/g.
Next, we calculate the mass of tretinoin added: 50mg.
Finally, we calculate the total mass of the resultant mixture: 20g (original gel) + 50mg (tretinoin) = 20.05g.
To find the resultant percentage strength, we divide the mass of tretinoin added by the total mass of the mixture and multiply by 100: (50mg/20.05g) x 100 = 0.249%.
Therefore, the resultant percentage strength is approximately 0.249%.