word problem

Question

You need a 35% alcohol solution. On hand, you have a 175 mL of a 85% alcohol mixture. How much pure water will you need to add to obtain the desired solution?

You will need

______mL of pure water
to obtain

_______mL of the desired 35% solution.

Answer 1

If a solution is 85% alcohol, then it is 85% alcohol and 15% something else (in this case water).  You need to add pure water (0% alcohol) to turn the solution into 35% alcohol and 65% water.

 

Notice that you are not taking any liquid out and only adding non-alcohol liquid, so the amount of alcohol in the solution will remain unchanged.

 

85% of 175 mL = 0.085(175)=148.75.  This means there is 148.75 mL of alcohol in the current solution, and that the 35% solution will also have 148.75 mL.

 

We can find the new amount of solution by solving the equation 0.35x = 148.75.

Dividing by 0.35, x = 425.

 

When all is said and done, you will have 425 mL of 35% solution, which means you added 425 - 175 or 250 mL of pure water. 

Answer 2

Let x = amount of water to add

(x ml)(0% alcohol) + (175 ml)(85% alcohol) = (175 + x ml)(35% alcohol)

14,875 = 6125 + 35x

35x = 8750

x = 250 mls of water needs to be added to obtain 425 mls of 35% alcohol