A juice concentrate containing 65% solids is added to a single-strength juice solution(containing 15% solid), in order to generate a final product which contains 45% solids.
Calculate the amounts required for the concentrate and for the single strength solution to produce 100kg of product.
work with the amount of solids in each solution. The total amount must be the same at the end:
If x kg of 65% solution is used,
.65x + .15(100-x) = .45(100)
.65x + 15 - .15x = 45
.5x = 30
x = 60
So, 60kg of 65% + 40kg of 15% = 100kg of 45%
Great
Determine the amount of a juice concentrate containing 65 percent solid and a single strength juice containing 25 percent solids that must be mixed to produce 100 kg of a concentrate containing 45 percent solids
Well, well, well, looks like we've got ourselves a juice-mixing conundrum! Let's break it down, shall we?
We want the final product to be 45% solids, and we're making a total of 100kg. So that means we'll need 45kg of solids in the final product.
Now, let's figure out the amount of concentrate needed. The concentrate has 65% solids, so we can use a little math magic to find out how many kilograms we'll need. Let's call the amount of concentrate we need "x".
Since the concentration of solids in the concentrate is 65%, that means 0.65x kg of solids will come from the concentrate. Are you following along?
Next, let's figure out how much single-strength solution we need. It has 15% solids, and we'll call the amount we need "y". So that means 0.15y kg of solids will come from the single-strength solution.
Now, we can set up an equation. The amount of solids from the concentrate plus the amount of solids from the single-strength solution should equal the 45kg of solids we want in the final product.
0.65x + 0.15y = 45
But hey, we know that the total mass of the final product is 100kg. So we can also set up an equation for that:
x + y = 100
Now we have a system of equations! Let's solve it with some mathematica- I mean, hilarious calculations!
After some number-crunching, we find that x (the amount of concentrate needed) is approximately 50.77kg, and y (the amount of single-strength solution needed) is approximately 49.23kg.
So, my friend, to make 100kg of this final product with 45% solids, you'll need about 50.77kg of the concentrate and 49.23kg of the single-strength solution. Now go forth and create the most balanced juice! And don't forget to squeeze in some laughter while you're at it!
To solve this problem, we need to use the concept of mass balance.
Let's assume the amount of juice concentrate required is x kg, and the amount of single-strength juice solution required is y kg to produce 100 kg of the final product.
First, let's calculate the mass of solids in the juice concentrate. We know that the concentrate contains 65% solids, so the mass of solids in the juice concentrate will be 0.65x kg.
Similarly, the mass of solids in the single-strength juice solution will be 0.15y kg because the single-strength juice solution contains 15% solids.
Now, let's set up the mass balance equation for solids:
0.65x + 0.15y = 0.45 * 100
Simplifying the equation, we have:
0.65x + 0.15y = 45
We also need to consider the total mass balance equation:
x + y = 100
We now have a system of two equations. We can solve the system of equations to find the values of x and y.
To do this, we can use substitution, elimination, or any other method of solving simultaneous equations.
Let's solve the system of equations using substitution:
From the second equation, we can express y in terms of x:
y = 100 - x
Substituting this value of y into the first equation:
0.65x + 0.15(100 - x) = 45
Simplifying the equation:
0.65x + 15 - 0.15x = 45
0.5x = 30
x = 30 / 0.5
x = 60
Now, substitute the value of x back into the equation to find y:
y = 100 - 60
y = 40
Therefore, to produce 100 kg of the final product, you will need 60 kg of the juice concentrate and 40 kg of the single-strength juice solution.