Use the concentrations of the given solution the final solution to write an equation.
A
Practice makes perfect
A pharmacist has 50 ounces of a 15 %, or 0.15, saline solution. They want to make a 10 %, or 0.10, saline solution by adding pure water. Let x represent the amount of pure water needed (in ounces). Then 50+x is the weight of the resulting solution. We can summarize what we know in a table.
Saline
Water
Saline
Weight (oz)
50
x
50+x
Concentration
0.15
0
0.10
A concentration of 0.15 means that there are 0.15 ounces of salt in 1 ounce of the saline. This also means that there are 0.15(50) ounces of salt in the original saline. Let's find how much this is.
0.15(50) = 7.5 oz
Now, there are 0.10(50+x) ounces of salt in the final saline solution. This is the same as the initial amount of salt in the solution. We know this because no salt was added or subtracted in the process — only water.
7.5 =0.10(50+x)
Let's solve the resulting equation for x to find out how much water was added.
