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
.85x +.60*150 = .80(150+x)
37.5 ml
To solve this problem, we need to use the concept of the weighted average. Here's how we can calculate the required amount of syrup containing 85% sucrose:
Let's assume that x represents the amount (in ml) of syrup containing 85% sucrose that needs to be mixed.
1. Calculate the amount of sucrose in the 60% syrup:
Amount of sucrose in the 60% syrup = 150 ml × 0.6
2. Calculate the amount of sucrose in the 85% syrup:
Amount of sucrose in the 85% syrup = x ml × 0.85
3. Calculate the total amount of sucrose in the final mixture:
Total amount of sucrose = Amount of sucrose in the 60% syrup + Amount of sucrose in the 85% syrup
4. Set up the equation:
Total amount of sucrose = 150 ml × 0.6 + x ml × 0.85
5. Set up the equation for the desired concentration:
Total amount of sucrose = (150 ml + x ml) × 0.8
Now, we can set these two equations equal to each other:
150 ml × 0.6 + x ml × 0.85 = (150 ml + x ml) × 0.8
Simplifying the equation:
90 + 0.85x = 0.8x + 120
Now, we can solve for x:
0.85x - 0.8x = 120 - 90
0.05x = 30
x = 30 / 0.05
x = 600 ml
Therefore, 600 ml of syrup containing 85% sucrose needs to be mixed with 150 ml of syrup containing 60% sucrose to make a syrup containing 80% sucrose.