How much of a 12% saline solution should be mixed with a 4% saline solution to obtain 40 milliliters of a 6% saline solution?. Use a system of equations and elimination method to solve. can someone please see if I am on the right track.
12T + 4F=6x40
-4 -4F 4
8T=2x40
8T=80
8T/8=80/8
T=10 ml
First of all, you always define your variables.
I deduced from your work that you:
let the amount of 12% solution used be T ml
let the amount of 4% solution used be F ml
clearly T + F = 40 is our first equation
( don't see that anywhere)
then .12T + .04F = .06(40)
times 100
12T + 4F = 240
or, dividing by 4 ....
3T + F = 60 , again, where is that equation?
(you had 12T + 4T = 6(40)
which is correct but I don't know how you are using it.
the line -4 -4f 4 below it means nothing to me)
so we have 2 equations:
3T + F = 60
T + F = 40
since we are to use elimination, subtract them
2T = 20
T = 10
back in T+F=40
10+F =40
F = 30
They should use 10 ml of the 12%, and 30 ml of the 4% solution.
You did get T = 10, but did not finish the question.
Your instructions were to use elimination, thus you needed two equations.
Yes, you are on the right track! Let's break down the steps to see if your solution is correct.
First, let's define our variables:
T = the amount (in milliliters) of 12% saline solution
F = the amount (in milliliters) of 4% saline solution
Now, let's set up the system of equations based on the given information:
Equation 1: The sum of the volumes of the 12% and 4% saline solutions is equal to 40 milliliters.
T + F = 40
Equation 2: The concentration of the final 6% saline solution is given by the weighted average of the concentrations of the two solutions.
(0.12T + 0.04F) / (T + F) = 0.06
Now, let's solve the system of equations using the elimination method:
Multiply equation 1 by -0.04 to match the coefficients of F in both equations:
-0.04(T + F) = -0.04(40)
-0.04T - 0.04F = -1.6
Now add this new equation to equation 2 to eliminate F:
(-0.04T - 0.04F) + (0.12T + 0.04F) = -1.6 + 0.06
Simplifying, we get:
0.08T = -1.54
Now, divide by 0.08 on both sides of the equation:
T = -1.54 / 0.08
T ≈ 10 ml
So, your result of T = 10 ml is correct! This means that you would need to mix 10 ml of the 12% saline solution with 30 ml (40 - 10) of the 4% saline solution to obtain 40 milliliters of a 6% saline solution.