you need to prepare 180g of an 5%cream using 30% stock cream and a cream base.how much is needed for each?
To find out how much of the 30% stock cream and cream base is needed, we'll need to use a simple equation based on the principle of proportions.
Let's assume x represents the amount of 30% stock cream needed in grams and y represents the amount of cream base needed in grams.
Given that the target cream has 5% fat, we can set up the equation:
0.05 * 180g = 0.30x + y
Simplifying the equation:
9g = 0.30x + y
Since we have two unknowns (x and y), we'll need another equation to solve the system.
The cream base is considered fat-free, so it contains 0% fat. The 30% stock cream is already given, so we can write a second equation:
x + y = 180g
Now, we have a system of linear equations that we can solve using substitution or elimination to find the values of x and y.
Let's solve it using substitution:
From the second equation, we have y = 180g - x
Substituting y in the first equation:
9g = 0.30x + (180g - x)
9g = 180g - 0.70x
0.70x = 180g - 9g
0.70x = 171g
Now we can solve for x:
x = 171g / 0.70
x ≈ 244.29g
Now, substitute the value of x back into the second equation to find y:
244.29g + y = 180g
y = 180g - 244.29g
y ≈ -64.29g
Since we cannot have a negative amount of cream base, it is not possible to prepare 180g of a 5% cream using the given 30% stock cream and cream base.