Salt, pepper and everything nice

Algebra Level pending

A chemist tries to invent a tasteful solution. He added a tablespoon of pepper and a spoonful of salt into 400 ml of water. The concentration of solution is 50%. Now he adds thrice the amount of salt and pepper. What is the increase in concentration?

25 80 10 30

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1 solution

Donglin Loo
Sep 15, 2014

Let the amount of a tablespoon pepper and a spoon salt be x g.

Using the formula of percentage by mass= M a s s o f s o l u t e M a s s o f s o l u t i o n × 100 % = M a s s o f s o l u t e M a s s o f s o l u t e + M a s s o f s o l v e n t × 100 % \frac{Mass of solute}{Mass of solution}\times100\%=\frac{Mass of solute}{Mass of solute+Mass of solvent}\times100\% ,

We have

x x + 400 × 100 % = 50 % \frac{x}{x+400}\times100\%=50\%

x x + 400 = 1 2 \frac{x}{x+400}=\frac{1}{2}

2 x = x + 400 2x=x+400

x = 400 x=400

Hence, the mass of solute (a tablespoon pepper and a spoon salt)= 400 g 400g

The concentration later= 400 × ( 3 + 1 ) 400 × ( 3 + 1 ) + 400 × 100 % = 1600 2000 × 100 % = 80 % \frac{400\times(3+1)}{400\times(3+1)+400}\times100\%=\frac{1600}{2000}\times100\%=80\%

So, the change in concentration (percentage by mass)= 80 % 50 % = 30 % 80\%-50\%=30\%


Note: Unless it is stated in the question, all the solute added cannot be extracted.

So, the concentration later= 400 × ( 3 + 1 ) 400 × ( 3 + 1 ) + 400 × 100 % = 1600 2000 × 100 % = 80 % , \frac{400\times(3+1)}{400\times(3+1)+400}\times100\%=\frac{1600}{2000}\times100\%=80\%,

instead of the concentration later= 400 × 3 400 × 3 + 400 × 100 % = 1200 1600 × 100 % = 75 % . \frac{400\times3}{400\times3+400}\times100\%=\frac{1200}{1600}\times100\%=75\%.

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