Question

Kim needs to add a 6% saline solution to an IV bag that contains 20 cubic centimeters of 10% saline solution.

Answer 1

Let 'x' represent the volume of 6% saline solution
Let 'y' represent the volume of 8% saline solution

Form 2 equations.
Eq. 1: 20+x=y
Meaning 20 cm³ + x cm³=y cm³
Eq 2: 0.06x+0.1(20)=0.08y
Meaning: 6% of x + 10% of 20= 8% of y

Use substitution or elimination to solve this linear system. I used substitution.
Sub. Eq. 1 (20+x=y)  into Eq. 2 (0.06x+0.1(20)=0.08y)
0.06x+ 0.1(20)=0.08(20+x)
0.06x+2+1.6=0.08x
-0.02x= -0.4
x=20

Substitute x=20 into equation 1 (you can also use 2 but in this case equation 1 is simpler)

20+x=y
20+20=y
40=y

To check, substitute x=20 and y=40 into equation 2

0.06x + 0.1(20)= 0.08y
0.06(20) +2 = 0.08(40)
1.2+2= 3.2
3.2=3.2

Therefore, Kim would need 20cm³ of 6% saline solution and 40cm³ of 10% saline solution to make 8% solution.