Calculate the percentage strength of hydrocortisone if you combine 30 g of 1%, 45 g of 0.5%, and 15 g of 2%. Round to the hundredth.
you know, all these mixture problems are done the same way.
If you have x ml of p% solution and y ml of q%, making z ml of r% solution,
px + qy = rz
Naturally, z = x+y
Now, plug in your numbers and show us whatcha got. By now you've been through all the variations. If you want confirmation, show us your solution. If you get stuck, show us where. Otherwise, . . .
To calculate the percentage strength of hydrocortisone after combining the given quantities, we need to calculate the total amount of hydrocortisone in grams and then determine the percentage strength.
Step 1: Calculate the total amount of hydrocortisone in grams.
For the 30 g of 1% hydrocortisone, we have:
1% = 1/100 = 0.01 (as a decimal)
Amount of hydrocortisone = 30 g × 0.01 = 0.3 g
For the 45 g of 0.5% hydrocortisone, we have:
0.5% = 0.5/100 = 0.005 (as a decimal)
Amount of hydrocortisone = 45 g × 0.005 = 0.225 g
For the 15 g of 2% hydrocortisone, we have:
2% = 2/100 = 0.02 (as a decimal)
Amount of hydrocortisone = 15 g × 0.02 = 0.3 g
Step 2: Calculate the total amount of hydrocortisone in grams from all the sources.
Total amount of hydrocortisone = 0.3 g + 0.225 g + 0.3 g = 0.825 g
Step 3: Calculate the combined percentage strength of hydrocortisone.
Combined percentage strength = (Total amount of hydrocortisone / Total amount of mixture) × 100
Total amount of mixture = 30 g + 45 g + 15 g = 90 g
Combined percentage strength = (0.825 g / 90 g) × 100 ≈ 0.917 % (rounded to the hundredth)
Therefore, the combined percentage strength of hydrocortisone is approximately 0.917%.
To calculate the percentage strength of hydrocortisone when you combine different concentrations, you need to consider both the quantity and concentration of each component.
First, let's convert the percentages to decimal values:
1% = 0.01
0.5% = 0.005
2% = 0.02
Next, we'll calculate the amount of hydrocortisone in each component:
30 g of 1% hydrocortisone = (30 g) x (0.01) = 0.3 g
45 g of 0.5% hydrocortisone = (45 g) x (0.005) = 0.225 g
15 g of 2% hydrocortisone = (15 g) x (0.02) = 0.3 g
Now, add up the total amount of hydrocortisone:
Total hydrocortisone = 0.3 g + 0.225 g + 0.3 g = 0.825 g
Lastly, we'll calculate the percentage strength:
Percentage strength = (Total hydrocortisone / Total weight) x 100
Total weight = 30 g + 45 g + 15 g = 90 g
Percentage strength = (0.825 g / 90 g) x 100 = 0.917 x 100 ≈ 91.67%
Hence, when you combine 30 g of 1%, 45 g of 0.5%, and 15 g of 2% hydrocortisone, the percentage strength would be approximately 91.67%.