You need 715 mL of a 45% alcohol solution. On hand, you have a 55% alcohol mixture. How much of the 55% alcohol mixture and pure water will you need to obtain the desired solution?

.55 a = .45(715)

585

To determine how much of the 55% alcohol mixture and pure water you will need, we can set up an equation based on the concentration and volume of the solution.

Let's assume you need "x" mL of the 55% alcohol mixture and "y" mL of pure water.

Now, let's set up the equation based on the amount of alcohol in each component:

Alcohol in the 55% mixture: 55/100 * x mL
Alcohol in the pure water: 0/100 * y mL (since pure water contains no alcohol)

The total amount of alcohol in the desired solution is given as 715 mL * 45/100 = 322.5 mL.

So, we have the equation:
55/100 * x + 0/100 * y = 322.5

Simplifying the equation, we get:
0.55x = 322.5

Now, solve for x:
x = 322.5 / 0.55
x ≈ 586.364 mL

Therefore, you will need approximately 586.364 mL of the 55% alcohol mixture.

To find the amount of pure water needed, you can subtract the amount of the 55% alcohol mixture from the desired volume:
y = 715 mL - 586.364 mL
y ≈ 128.636 mL

Therefore, you will need approximately 128.636 mL of pure water.

To solve this problem, we can use the concept of mixing two solutions.

Let's assume that you need x milliliters of the 55% alcohol mixture.

Now, let's break down the problem into two parts:

1. Alcohol content equation:
The total amount of alcohol in the 55% alcohol mixture is 0.55x milliliters.

2. Water content equation:
Since you need a total of 715 mL of the final solution and x mL of the 55% alcohol mixture, the remaining amount will be water. Therefore, the water content will be (715 - x) mL.

Now, let's set up an equation for the overall alcohol content in the final solution:

Alcohol in the 55% mixture + Alcohol in the water = Alcohol in the final solution

0.55x + 0 = 0.45(715)

Simplifying the equation, we have:

0.55x = 0.45(715)
0.55x = 321.75
x = 321.75/0.55
x ≈ 585

So, you would need approximately 585 mL of the 55% alcohol mixture.

To find the amount of water needed, we can subtract x from the total volume needed:

Amount of water = Total volume - Amount of 55% alcohol mixture
Amount of water = 715 mL - 585 mL
Amount of water ≈ 130 mL

Therefore, you would need approximately 585 mL of the 55% alcohol mixture and 130 mL of water to obtain the desired 715 mL of a 45% alcohol solution.