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

X is the amount of water.

85% = 0.85 and 35% = 0.35

 

The alcohol content is then:

 

175* 0.85 + X*0% = (X+175)*0.35

 

148.75                  = 0.35 X + 61.25 <--- distributive, right side; 0% cancels on the left

 

87.5 = 0.35X <--- subtracts 61.25 from both sides

 

8750 = 35X <--- multiplies both sides by 100 to clear the decimals

 

X = 8750/35 = 250  <--- solves for x

 

CHECK:

 

175*.85 = 148.75 mL of alcohol on hand in the original mixture

 

175 + 250  = 425

 

148.75/425 = .35 = 35%