# Help with Math WordProblem

• Feb 10th 2011, 11:51 AM
thelensboss
Help with Math WordProblem
A 1000L Tank contains 50L of a 25% brine solution. You add x liters of a 75% brine solution to the ank.
a)Show that the concentration C, the proportion of brine to total solution, in the final mixture is:
C= (3x+50)/(4(x+50))
b)Determine the domain of the function based on the physical constraints of the problem. Explain your answer.
c) Graph the concentration function. As the tank is filled, what happens to the rate at which the concentration of brine is increasing? What percent does the concentration of brine appear to approach?
• Feb 10th 2011, 12:02 PM
Quote:

Originally Posted by thelensboss
A 1000L Tank contains 50L of a 25% brine solution. You add x liters of a 75% brine solution to the ank.
a)Show that the concentration C, the proportion of brine to total solution, in the final mixture is:
C= (3x+50)/(4(x+50))
b)Determine the domain of the function based on the physical constraints of the problem. Explain your answer.
c) Graph the concentration function. As the tank is filled, what happens to the rate at which the concentration of brine is increasing? What percent does the concentration of brine appear to approach?

1000 litres is simply the capacity of the tank.

The total solution is 50 litres plus x litres

$25\%=\frac{25}{100}=\frac{1}{4}$

$75\%=\frac{3}{4}$

Therefore, the amount of brine in the solution, in litres, is

$\frac{1}{4}(50)+\frac{3}{4}(x)$

Try writing the fraction of brine divided by total amount of solution.
• Feb 10th 2011, 12:34 PM
thelensboss
alright how about the domain based on physical constraints of the problem
• Feb 10th 2011, 12:37 PM
The physical constraint relates on the fact that the solution cannot exceed 1000 litres.
That creates an upper bound for x.
The maximum value of the solution reveals the domain.
• Feb 10th 2011, 12:49 PM
thelensboss
So is the domain X cant equal -50 cuz that doesnt make sense
• Feb 10th 2011, 12:52 PM
No, x can't be negative at all, since a measurement in litres cannot drop below zero.

The solution of 50+x litres cannot exceed 1000 litres.
• Feb 10th 2011, 12:58 PM
thelensboss
Yea so it is basically x must equal 950 or less??

And also can you answer the last question part c because when I graphed it on my calc it did not show
• Feb 10th 2011, 01:13 PM
As x increases towards 950 (and beyond if it was physically possible), the graph approaches $\frac{3x}{4x}=\frac{3}{4}$