Stain remover solution word problem

Question

katy runs a dry cleaning business and needs 6% phosphoric acid solution to remove a stain from a suit. Katy has on hand 14% phosphoric acid solution and a 2% phosphoric acid solution. How many milliliters of each of these solutions should katy mix to obtain 45 milliliters of a 6% phosphoric acid solution?

Answer 1

First, we will convert the % figures to decimals, so 2% = 0.02, 6% = 0.06, and 14% = 0.14

 

let x = amount of 2% solution; then 45ml - x will equal the amount of 14% solution

 

our equation will be 0.02x + 0.14(45ml - x) = 45ml(0.06)

 

expanding, 0.02x + 6.3ml - 0.14x = 2.7ml

 

combining, we get -0.12x = 2.7ml - 6.3ml, which becomes -0.12x = -3.6ml

 

multiply both sides by -1 to get 0.12x = 3.6ml

divide both sides by 0.12 to get x = 30ml

 

So, 30ml of 2% plus 15ml of 14% will yield 45ml of 6%

 

Proof: 30ml x 0.02 + 15ml x 0.14  = 45ml x 0.06

0.6 + 2.1 = 2.7