To prepare 100 g of a 5% cream, how much 3% and 6% cream is needed?

To determine how much of the 3% and 6% creams are needed to prepare 100 g of a 5% cream, a method called alligation can be applied. This method allows one to find the required proportions of the two different concentrations to achieve a desired concentration.

First, consider the desired concentration of the final mixture (5%) and the concentrations of the available creams (3% and 6%). The alligation setup would look like this:

1. Subtract the lower concentration (3%) from the desired concentration (5%):

• 5% - 3% = 2%

2. Then, subtract the desired concentration (5%) from the higher concentration (6%):

• 6% - 5% = 1%

Now, you can establish a ratio from the results:

• The portion of the 3% cream needed corresponds to the difference from the higher concentration (1), while the portion of the 6% cream corresponds to the difference from the lower concentration (2). Thus, the ratio of the creams is 1:2.

Next, when you sum the parts of the ratio (1 + 2 = 3), you can calculate the proportions of each cream needed: