how many grams of 2.5% hydrocortisone cream should be mived with 360 g of 0.25 to make a 1% hydrocortisone cream
180
So what is the answer ?
Well, mixing creams sounds like a lot of fun! Let's get the math party started.
To find out how many grams of the 2.5% hydrocortisone cream we should mix, let's use a little equation action:
(grams of 2.5% hydrocortisone cream) + (grams of 0.25% hydrocortisone cream) = (total grams of 1% hydrocortisone cream)
So, we have:
(2.5%)(x) + (0.25%)(360g) = (1%)(360g + x)
Now, let's shuffle some numbers around and solve for "x", which represents the grams of the 2.5% hydrocortisone cream:
0.025x + 0.25(360) = 0.01(360 + x)
Multiply everything by 100 to get rid of those pesky decimals:
2.5x + 25(360) = 1(360 + x)
Now, after some intense math gymnastics, we find:
1.5x = 5900
Divide both sides by 1.5:
x ≈ 3933
So, you should mix approximately 3933 grams of the 2.5% hydrocortisone cream with the 360 grams of 0.25% hydrocortisone cream to make a 1% hydrocortisone cream. Time to bust out those mixing bowls and get to work!
To solve this problem, we need to use a basic formula for mixing two solutions to get a desired concentration. The formula is:
C1 x V1 + C2 x V2 = C3 x (V1 + V2)
where:
- C1 is the concentration of the first solution
- V1 is the volume of the first solution
- C2 is the concentration of the second solution
- V2 is the volume of the second solution
- C3 is the concentration of the resulting mixture
In this case, we have:
- C1 = 2.5% (hydrocortisone cream)
- V1 is what we need to find
- C2 = 0.25% (hydrocortisone cream)
- V2 = 360 g (0.25% hydrocortisone cream)
- C3 = 1% (hydrocortisone cream)
Substituting these values into the formula, we get:
2.5% x V1 + 0.25% x 360g = 1% x (V1 + 360g)
Now let's solve for V1 (the volume of 2.5% hydrocortisone cream needed):
0.025V1 + 0.0025 x 360 = 0.01V1 + 0.01 x 360
0.025V1 + 0.0025 x 360 = 0.01V1 + 3.6
0.025V1 - 0.01V1 = 3.6 - 0.0025 x 360
0.015V1 = 3.6 - 0.9
0.015V1 = 2.7
V1 = 2.7 / 0.015
V1 = 180
Therefore, you will need to mix 180 grams of 2.5% hydrocortisone cream with 360 grams of 0.25% hydrocortisone cream to make a 1% hydrocortisone cream.
By proportion, you get
2.5%-1%=1.5
1%-0.25%=0.75
Ratio=1.5:0.75=2:1
To make the mixture, we use the inverse of the ratio, therefore
Mixture=1:2, or
120g of 2.5% and 240g of 0.25% make 360g of 1% (assuming both have same density).
Check: (120*.025+240*.0025)/360=1%
You can also solve this algebraically:
Let x=number of grams of 2.5%, then
360-x=number of grams of 0.25%
We want
0.025x+0.0025*(360-x)=360*0.01
0.0225x=3.6-0.9=2.7
x=2.7/0.0225=120g of 2.5%
(360-x)=240g of 0.25%