Answer:
10mL of the 5% solution and 40mL of the 10% solution
Step-by-step explanation:
To get the amount of each solution in milliliters that must be mixed to male 50ml of a 9% solution,
First let us represent the amount of 5% solution as A
Furthermore, let us represent the amount of 10% solution as B
From the question we know that A + B = 50ml
Hence 5% = 0.05 and 10% = 0.10
Then we get
0.05A + 0.10B = 0.09(A+B)
Then we solve further to get
Also, from A+B=50
A = 50 - B
0.05(50 - B) + 0.1B = 0.09(50 - B + B)
2.5 - 0.05B + 0.1B = 4.5
0.05B = 2
B = 40mL
And we know that A+B = 50,
Hence
40+A = 50
A= 50-40 = 10mL
By solving a system of equations, we will see that we must use 40 ml of the 10% solution and 10 ml of the 5% solution.
First, we need to define the variables that we will be using.
We know that we want to make 50ml of solution, then:
x + y = 50
And that solution must have a concentration of 9%, so the concentration in the left side must be the same one as on the right side, so we get the equation:
0.05*x + 0.10*y = 0.09*50
Then we got a system of equations:
x + y = 50
0.05*x + 0.10*y = 0.09*50
To solve this, first we need to isolate one of the variables in one of the equations, I will isolate x on the first one to get:
x = 50 - y.
Replacing that on the other equation we get:
0.05*(50 - y) + 0.10*y = 0.09*50
2.5 - 0.05*y + 0.10*y = 4.5
2.5 + 0.05*y = 4.5
0.05*y = 4.5 - 2.5 = 2
y = 2/0.05 = 40
Then we must use 40 milliliters of the 10% solutions, and the other 10 milliliters will be of the 5% solution
If you want to learn more about systems of equations, you can read:
https://brainly.com/question/13729904
