How much 30% alcohol, 45% alcohol, 60% alcohol and 95% alcohol could be mixed to make 200ml of alcohol?

the right answer 30% is 112.5ml
45% is 25ml
60% is 12.5ml
95% is 50ml
Who helps me step by step clearly

Please some professional tutor solve it

To solve this problem, we can use a technique called the method of alligation. This method allows us to find the proportions in which different concentrations of alcohol need to be mixed to obtain a desired concentration. Here's how you can solve this step by step:

Step 1: Assign variables to the concentrations of alcohol and the desired total volume.

Let:
x = volume of 30% alcohol (in ml)
y = volume of 45% alcohol (in ml)
z = volume of 60% alcohol (in ml)
w = volume of 95% alcohol (in ml)
v = total volume of alcohol (in ml), which is 200ml in this case.

Step 2: Write down the equation relating the sum of the volumes to the desired total volume:

x + y + z + w = v
x + y + z + w = 200 (since v = 200 ml)

Step 3: Set up an alligation diagram.

Draw a diagram with four columns, one for each concentration of alcohol: 30%, 45%, 60%, and 95%.

Step 4: Place the desired concentration (i.e., 30% alcohol) in the middle of the diagram.

30% is closer to 45% than to 60%.

Step 5: Set up ratios based on the differences between the desired concentration and the other concentrations.

For the 30% and 45% concentrations, the ratio is 15:30 or 1:2 (since 45% is 15% higher than 30%).
For the 30% and 60% concentrations, the ratio is 30:30 or 1:1 (since 60% is 30% higher than 30%).
For the 30% and 95% concentrations, the ratio is 65:30 or 13:6 (since 95% is 65% higher than 30%).

Step 6: Assign weights to the ratios based on the desired total volume.

Since the total volume is 200 ml, the sum of the weights will be equal to 200.

Let the weight for the 30% and 45% ratio be a.
Let the weight for the 30% and 60% ratio be b.
Let the weight for the 30% and 95% ratio be c.

Step 7: Write down the weighted ratios and set up equations.

You can write the following equations based on the weighted ratios:
2a = 200 (for the 30% and 45% ratio)
a + b = 200 (for the 30% and 60% ratio)
6c + a = 200 (for the 30% and 95% ratio)

Step 8: Solve the equations to find the values of a, b, and c.

From the first equation, we have:
a = 200/2 = 100

Plugging in this value into the second equation, we have:
100 + b = 200
b = 200 - 100 = 100

Plugging in the values of a and b into the third equation, we have:
6c + 100 = 200
6c = 200 - 100
6c = 100
c = 100/6

Therefore, a = 100 ml, b = 100 ml, and c ≈ 16.67 ml.

Step 9: Calculate the volume of each concentration by multiplying the weight by the corresponding ratio.

For the 30% alcohol concentration, we have:
30% * a = 30% * 100 = 30 * 100/100 = 30 ml

For the 45% alcohol concentration, we have:
45% * a = 45% * 100 = 45 * 100/100 = 45 ml

For the 60% alcohol concentration, we have:
60% * b = 60% * 100 = 60 * 100/100 = 60 ml

For the 95% alcohol concentration, we have:
95% * c ≈ 95% * 16.67 = 95 * 16.67/100 ≈ 15.84 ml

So, the volumes of each concentration needed are approximately:
30% alcohol: 30 ml
45% alcohol: 45 ml
60% alcohol: 60 ml
95% alcohol: 15.84 ml

Note that the exact values may vary slightly due to rounding.