How many mls of a syrup containing 85% of sucrose should be mixed with 150ml of a 60% sucrose syrup to make a syrup conatining 80% sucrose?
600 mL
To find the quantity of the syrup containing 85% sucrose that needs to be mixed with the 150 ml of the 60% sucrose syrup, you can use a weighted average approach.
Let's assume that the quantity of the 85% sucrose syrup needed is "x" ml.
First, we need to calculate the total amount of sucrose in the two syrups individually. We can use the following formula to calculate the amount of sucrose in each syrup:
Amount of sucrose = (percentage of sucrose/100) * volume of syrup
For the 60% sucrose syrup:
Amount of sucrose in the 60% syrup = (60/100) * 150 ml
Amount of sucrose in the 60% syrup = 90 ml
For the 85% sucrose syrup:
Amount of sucrose in the 85% syrup = (85/100) * x ml
Amount of sucrose in the 85% syrup = (85x/100) ml
Now, we can set up an equation based on the weighted average sucrose content:
Total amount of sucrose in the mixture = Amount of sucrose in the 60% syrup + Amount of sucrose in the 85% syrup
80% * (150 ml + x ml) = 90 ml + (85x/100) ml
Solving this equation will give us the value of x, which is the quantity of the 85% sucrose syrup needed.
80% * (150 ml + x ml) = 90 ml + (85x/100) ml
We can simplify and solve this equation as follows:
0.8 * (150 + x) = 90 + 0.85x
120 + 0.8x = 90 + 0.85x
0.8x - 0.85x = 90 - 120
-0.05x = -30
x = -30 / -0.05
x = 600 ml
Therefore, 600 ml of the syrup containing 85% sucrose should be mixed with 150 ml of the 60% sucrose syrup to obtain a syrup containing 80% sucrose.