ineedtocheathelpme
Answered

Westonci.ca is your trusted source for finding answers to a wide range of questions, backed by a knowledgeable community. Get quick and reliable solutions to your questions from a community of seasoned experts on our user-friendly platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

.A tank contains seven liters of 10% alcohol solution. How many liters of 6% alcohol solution should be added to have 8% alcohol solution?​

Sagot :

facundo3141592

Answer: 7 liters of 6% alcohol solution.

Step-by-step explanation:

We have 7 liters of 10% alcohol solution, and in this the total amount of alcohol is

A = (10%/100%)*7 L = 0.1*7L = 0.7L

Now, suppose that we add N liters of 6% alcohol solution, then we have a total of:

(N + 7) Liters

And the total amount of alcohol would be:

(6%/100%)*N + 0.7L

0.06*N + 0.7L

The quotient between the total volume of alcohol and the total volume of liquid needs to be 0.08 (because we want a percentage of 8% of alcohol, and the decimal form of 8% is 0.08)

Then:

(0.06*N + 0.7L)/(N + 7L) = 0.08

We want to sove this for N

(0.06*N + 0.7L) = 0.08*(N + 7L)

0.06*N + 0.7L = 0.08*N + 0.56L

0.7L - 0.56L = 0.08*N - 0.06*N

0.14 L = 0.02*N

0.14L/0.02 = N = 7L

Then we need to add 7 liters of 6% alcohol solution.

The amount of 6% alcohol solution should be added to 7 liters of 10% alcohol solution to have 8% alcohol solution is 7 liters.

What is an equation?

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Let the amount of 6% mixed in the 10% alcohol be x.

We know that the total solution is 7 liter of 10% alcohol, and x liters of 6% alcohol. And we need to make 8% alcohol solution, therefore, the total alcohol in the mixed solution can be written as,

[tex](10\%\ of\ 7\ liters) + (6\%\ of\ x\ liters) = (8\%\ of\ Total\ solution)\\\\(0.10 \times 7)+(0.06 \times x) = 0.80(7+x)\\\\0.7 + 0.06x = 0.56 +0.08x\\\\0.14 = 0.02x\\\\x = 7[/tex]

Hence, the amount of 6% alcohol solution should be added to 7 liters of 10% alcohol solution to have 8% alcohol solution is 7 liters.

Learn more about Equation:

https://brainly.com/question/2263981

Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.