a pharm tech needs to prepare 100g of 3% cream using 1% and 5% how much grams required to compound this medication. i have the answer but need the formula. is this a alligation
Yes, this problem can be solved using alligation.
To prepare a 3% cream using 1% and 5%, we need to determine the ratio of each ingredient needed.
1. Set up a diagram with the percentages on top and the amount of each ingredient on bottom:
1% --- x grams of 1% cream
5% --- y grams of 5% cream
3% --- 100g of 3% cream (total amount needed)
2. Draw a line between the 1% and 3% rows, and another line between the 5% and 3% rows.
1% --- x grams of 1% cream
---------------------------------
5% --- y grams of 5% cream
---------------------------------
3% --- 100g of 3% cream (total amount needed)
3. Subtract the percentages diagonally to find the difference. For example, to get from 1% to 3%, we need an increase of 2%. To get from 5% to 3%, we need a decrease of 2%.
1% --- x grams of 1% cream
---------2%---------------------
5% --- y grams of 5% cream
--------------2%----------------
3% --- 100g of 3% cream (total amount needed)
4. Place the values in the diagram, with the larger percentage on top of the diagonal and the smaller percentage on bottom:
1% --- x grams of 1% cream
---------2%---------------------
5% --- y grams of 5% cream
--------------2%----------------
3% --- 100g of 3% cream (total amount needed)
| 2 |
|------------------|
| 4 |
5. Add the values in each column to get the total amount of each cream needed:
1% --- x grams of 1% cream
---------2%---------------------
5% --- y grams of 5% cream
--------------2%----------------
3% --- 100g of 3% cream (total amount needed)
| 2 | | 4 |
|------------------| x + |----------------| y = 100g
| 4 | | 4 |
6. Solve for x and y by cross-multiplying and simplifying the equation:
2x + 4y = 400
x + 2y = 200
Multiply the second equation by 2:
2x + 4y = 400
2x + 4y = 400
Subtract the second equation from the first:
0 = 0
This means that the equation is consistent, and any value of x and y that satisfy the second equation will work.
To find the actual amount of each cream needed, we can use the ratios from the second equation:
x + 2y = 200
If we assume x = 1g (the smallest amount possible), then:
1 + 2y = 200
2y = 199
y = 99.5g
So we need 1g of 1% cream and 99.5g of 5% cream to make 100g of 3% cream.
Check:
(1% x 1g) + (5% x 99.5g) = (0.01 x 1g) + (0.05 x 99.5g) = 5.025g
(5.025g / 100g) x 100% = 3.0%, which is the desired concentration.