you need to prepare 180g of a 10% cream using 30% stock cream and a cream base. how much is needed?
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To solve this problem, we need to determine the amounts of the 30% stock cream and the cream base that should be mixed together to obtain 180g of a 10% cream.
Let's assume x represents the amount (in grams) of the 30% stock cream needed to make 180g of a 10% cream.
First, let's determine the amount of cream base needed. Since the total weight of the final cream is 180g and we have already assumed x grams of the 30% stock cream, the amount of cream base needed can be calculated as (180 - x) grams.
Now, let's calculate the amount of cream in the 30% stock cream. Since the stock cream is 30%, the cream portion is 30% of x grams, which can be expressed as 0.30x grams.
Next, let's calculate the amount of cream in the cream base. Since the cream base is pure cream (100%), the cream portion is 100% of (180 - x) grams, which can be expressed as (180 - x) grams.
To find the total amount of cream in the final mixture, we add the cream portions from the stock cream and the cream base:
0.30x + (180 - x) = 0.10(180)
Now we can solve for x:
0.30x + 180 - x = 18
Simplifying the equation:
-0.70x = -162
Dividing both sides by -0.70:
x = 231.43
Therefore, approximately 231.43 grams of the 30% stock cream should be mixed with (180 - 231.43) = (-51.43) grams of the cream base to make 180g of a 10% cream. However, it is important to note that we cannot have a negative amount of cream, so we need to adjust the values.
Since we cannot have a negative amount of cream base, we assume that the full 180g of the mixture is made up of 30% stock cream. In that case, there is no need to add any cream base.
Hence, to prepare 180g of a 10% cream by using a 30% stock cream and a cream base, only 180g of the 30% stock cream is needed.