How many quarts of water must be added to 18 quarts of a 32% alcohol solution to dilute it to a solution that is only 12% alcohol.
you want to dilute it 32/12 times, or 8/3 or 2.666 times. That means you want to add one part original, and 1.666 parts water.
one part= 18 quarts
1.666 parts= 30 parts water
To dilute the 18 quarts of a 32% alcohol solution to a solution that is 12% alcohol, we need to calculate the amount of water that needs to be added.
Step 1: Convert the percentages to decimals:
32% = 0.32
12% = 0.12
Step 2: Set up the equation:
(0.32 * 18) = (0.12 * (18 + x))
Here, x represents the number of quarts of water to be added.
Step 3: Solve for x:
0.32 * 18 = 0.12 * (18 + x)
5.76 = 2.16 + 0.12x
Step 4: Simplify the equation:
5.76 - 2.16 = 0.12x
3.60 = 0.12x
Step 5: Divide both sides by 0.12:
3.60 รท 0.12 = x
30 = x
Therefore, 30 quarts of water must be added to the 18 quarts of a 32% alcohol solution to dilute it to a solution that is only 12% alcohol.
To solve this problem, we need to determine the amount of water that needs to be added to the 18 quarts of 32% alcohol solution to obtain a 12% alcohol solution.
Let's break down the problem step-by-step:
Step 1: Understand the information given
- Initial solution: 18 quarts of a 32% alcohol solution
- Desired solution: A dilution that is only 12% alcohol
- Unknown: Amount of water to be added
Step 2: Set up the equation
Let's assume x represents the amount of water to be added (in quarts). The total volume of the solution after dilution will be 18 + x quarts.
The equation can be set up based on the alcohol content in the initial and desired solutions:
Alcohol in initial solution + Alcohol in water = Alcohol in final solution
(0.32 * 18) + (0 * x) = 0.12 * (18 + x)
Step 3: Solve the equation
Now, we will solve the equation to find the value of x, representing the amount of water that needs to be added:
5.76 + 0 = 2.16 + 0.12x
5.76 = 2.16 + 0.12x
5.76 - 2.16 = 0.12x
3.60 = 0.12x
Step 4: Calculate the answer
To find the value of x, divide both sides of the equation by 0.12:
3.60 / 0.12 = x
x = 30
Therefore, you need to add 30 quarts of water to the 18 quarts of 32% alcohol solution in order to dilute it to a 12% alcohol solution.