You need a 45% alcohol solution. On hand, you have a 150 mL of a 15% alcohol mixture. You also have 70% alcohol mixture. How much of the 70% mixture will you need to add to obtain the desired solution?

add up the amount of alcohol in each part. It must equal the alcohol in the final mixture:

.15*150 + .70x = .45(150+x)

To determine how much of the 70% alcohol mixture you will need to add, you can follow these steps:

Step 1: Calculate the amount of alcohol in the 15% mixture:
The 15% mixture contains 15% alcohol. So, the amount of alcohol in the 15% mixture can be calculated as:
Alcohol in 15% mixture = (15/100) * 150 mL

Step 2: Calculate the amount of alcohol needed in the final 45% solution:
Since you need a 45% alcohol solution, the amount of alcohol needed in the final solution can be calculated as:
Alcohol needed = (45/100) * (150 mL + X mL), where X is the amount of the 70% mixture needed.

Step 3: Solve for X:
Using the calculated values from Step 1 and Step 2, we can set up the equation:
(15/100) * 150 mL + (X mL) = (45/100) * (150 mL + X mL)

Step 4: Solve for X:
Simplifying the equation, we can solve for X:
22.5 mL + X mL = 67.5 mL + 0.45X
0.55X = 45 mL
X = 45 mL / 0.55
X ≈ 81.82 mL

So, you will need to add approximately 81.82 mL of the 70% alcohol mixture to obtain the desired 45% alcohol solution.

To solve this problem, we need to calculate how much of the 70% alcohol mixture should be added to the 150 mL of the 15% alcohol mixture to obtain a 45% alcohol solution.

Let's assume we need to add x mL of the 70% alcohol mixture.

First, we can calculate the amount of alcohol in the 150 mL of the 15% alcohol mixture:
Alcohol in the 15% mixture = (15/100) * 150 mL = 22.5 mL

Next, we can calculate the amount of alcohol in the x mL of the 70% alcohol mixture:
Alcohol in the x mL of 70% mixture = (70/100) * x mL = 0.7x mL

Now, let's calculate the total amount of alcohol in the final mixture:
Total alcohol in the final mixture = Alcohol in the 15% mixture + Alcohol in the x mL of 70% mixture

Since we want a 45% alcohol solution, we can set up the equation:
Total alcohol in the final mixture = (45/100) * (150 + x) mL

Now, we can set up the equation and solve for x:
22.5 mL + 0.7x mL = (45/100) * (150 + x) mL

To simplify the equation, we can multiply both sides by 100:
2250 + 70x = 45(150 + x)

Expanding the equation:
2250 + 70x = 6750 + 45x

Next, we can simplify the equation:
70x - 45x = 6750 - 2250
25x = 4500
x = 4500 / 25
x = 180

Therefore, you will need to add 180 mL of the 70% alcohol mixture to obtain the desired 45% alcohol solution.

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