How many mls of a syrup containing 85% of sucrose should be mixed with 150ml of a 60%sucrose syrup to make a syrup containing 80% sucrose?
.85x + .60*150 = .80(x+150)
.85x + 90 = .80x + 120
.05x = 30
x = 600
so, add 600ml of 85% syrup to 150ml of 60% syrup
Ah, the sweet science of syrup mixing! Let's get down to business, shall we?
To solve this syrupy problem, we can use a little math trickery. Since we want to end up with a syrup containing 80% sucrose, we can think of this as finding the "average" concentration between the two syrups.
So, let's call the amount of the 85% sucrose syrup we need to mix "x" (in ml). Now, we know that the total volume of syrup will be 150ml + x.
To figure out the final concentration, we'll multiply the volume of the 60% sucrose syrup (150ml) by its concentration (0.6), which gives us 90ml of pure sucrose. We'll do the same for the unknown syrup: (x ml) * (0.85 concentration) gives us 0.85x ml of pure sucrose.
Now, if we add those two amounts together, we'll have the total amount of pure sucrose in the final syrup:
90 + 0.85x
But we also know that the final syrup needs to be 80% sucrose. So, setting up an equation, we can say that:
(90 + 0.85x) / (150 + x) = 0.80
Now, let's get rid of those pesky decimals by multiplying through by 100:
90 + 0.85x = 0.80 * (150 + x)
Multiplying that out:
90 + 0.85x = 120 + 0.80x
Subtracting 0.80x from both sides:
0.05x = 30
Finally, dividing both sides by 0.05:
x = 600
So, you should mix 600ml of the 85% sucrose syrup with the 150ml of the 60% sucrose syrup to get the desired 80% sucrose syrup. Voila!
To solve this problem, let's assume that x milliliters of the 85% sucrose syrup should be mixed with the 150 mL of the 60% sucrose syrup.
Step 1: Calculate the amount of pure sucrose in the 85% syrup.
The 85% syrup contains 85% of sucrose, which means it contains 85/100 = 0.85 pure sucrose per milliliter. So, the amount of pure sucrose in x mL of the 85% syrup is 0.85x.
Step 2: Calculate the amount of pure sucrose in the 60% syrup.
The 60% syrup contains 60% of sucrose, which means it contains 60/100 = 0.6 pure sucrose per milliliter. So, the amount of pure sucrose in 150 mL of the 60%sucrose syrup is 0.6 * 150 = 90.
Step 3: Calculate the amount of pure sucrose in the final mixture.
The total amount of pure sucrose in the final mixture is the sum of the pure sucrose in the 85% syrup and the pure sucrose in the 60% syrup. So, we have 0.85x + 90.
Step 4: Calculate the amount of the final mixture.
The total amount of the final mixture is the sum of the volume of the 85% syrup and the volume of the 60% syrup. So, we have x + 150.
Step 5: Setup the equation.
The equation will be: (0.85x + 90) / (x + 150) = 0.80
Step 6: Solve the equation.
Let's solve the equation to find the value of x:
0.85x + 90 = 0.80(x + 150)
0.85x + 90 = 0.80x + 120
0.85x - 0.80x = 120 - 90
0.05x = 30
x = 30 / 0.05
x = 600
Step 7: Answer.
To make a syrup containing 80% sucrose, you should mix 600 mL of the 85% sucrose syrup with 150 mL of the 60% sucrose syrup.
To find the answer, we can use the concept of weighted averages.
Let's assume x represents the volume (in ml) of the 85% sucrose syrup that needs to be mixed.
The amount of sucrose in the 85% syrup can be calculated as 0.85x, and the amount of sucrose in the 60% syrup is 0.6 * 150 = 90 ml (as it is given that the volume of the 60% sucrose syrup is 150 ml).
Now, we need to find the total amount of sucrose in the 80% syrup. This can be given as follows:
0.85x + 90 ml = 0.8 * (x + 150 ml)
Simplifying the equation:
0.85x + 90 ml = 0.8x + 120 ml
Rearranging the terms:
0.85x - 0.8x = 120 ml - 90 ml
0.05x = 30 ml
Dividing both sides by 0.05:
x = 30 ml / 0.05
x = 600 ml
Therefore, you should mix 600 ml of the 85% sucrose syrup with the 150 ml of the 60% sucrose syrup to make a syrup containing 80% sucrose.