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2) [8 points] Benjamin wishes to strengthen a mixture that is 10% alcohol to
one that is 30% alcohol. How much pure alcohol should they add to 12L of
the 10% mixture?



Answer :

facundo3141592

you need to add 3.43 liters of pure alcohol to reach a concentration of 30%.

How much pure alcohol should they add to 12L of the 10% mixture?

Let's define the variable x as the number of liters of the 30% that you need to use.

The concentration of the mixture then will be:

1*x +  0.1*12

Where the concentration for the x liters is 100%, because this is pure alcohol, and for the 12 liters we use a concentration of 10%.

Now, that must be equal to a mixture with a concentration of the 30%, then we can write:

x + 0.1*12 = (x + 12)*0.3

Now we just need to solve this linear equation for x.

x + 1.2 = x*0.3 + 12*0.3

x - x*0.3 = 12*0.3 - 1.2

x*0.7 = 12*0.3 - 1.2

x = (12*0.3 - 1.2)/0.7 = 3.43

This means that you need to add 3.43 liters of pure alcohol to reach a concentration of 30%.

If you want to learn more about linear equations:

https://brainly.com/question/1884491

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