SOLUTION: From a full 50 liter container of a 40% conentration of acid, x liters is removed and replaced with 100% acid. - Write the amount of acid in the final mixture as a function of

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Question 1184000: From a full 50 liter container of a 40% conentration of acid, x liters is removed and replaced with 100% acid.
- Write the amount of acid in the final mixture as a function of x
--Determine the domain and range of the function.
Thanks!
Found 2 solutions by Theo, greenestamps:
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
yout total amount of solution is 50 liters.
the amount of acid is .4 * 50 = 20 liters.
if you take out x liters, you are taking out .4 * x liters of acid and you are putting back in 1 * x liters of acid.
your net gain is .6 * x liter of acid.
the amount of acid in the final solution is 20 + .6 * x.

for example:
assume x = 30
you take out 30 liters of 40% solution and replace it with 30 liters of 100% solution.
your net gain is 30 liters of 60% solution = 18 liters of acid.
your total acid is now 20 + 18 = 38 liters of acid.
you had 20 liters of acid in the solution.
you lost 30 * .4 = 12 liters of acid.
you added 30 liters of acid.
your total acid is 20 - 12 + 30 = 38 liters.
20 + .6 * 30 = 38

formula looks good.
the amount of acid you are left with is equal to 20 + .6 * x.

Answer by greenestamps(13200) (Show Source):
You can put this solution on YOUR website!

x liters will be the 100% acid that was added; (50-x) liters will be the original 40% acid. The total amount of acid will be

The domain is the number of liters that can be removed and replaced; obviously that is 0 to 50.

The function is linear, so the range is determined by the function values at the minimum and maximum values of the domain.
f(0)=20; f(50)=50. The range is 20 to 50.