I encountered the following problem:
10 grams of water is added to a 30% solution of barium chloride to dilute the solution to 20%. How many grams of the original solution did we start with?
The answer is 20 grams calculated as follows:
Let x = the number of grams of the original solution.
(0.20)(10+x) = 0.30x
x = 20
I then asked myself this question: How would the solution to this problem be changed if, instead of adding 10 grams of water to dilute the solution to 20%, 10 grams of barium chloride were added to strengthen the solution to 40%?
It seems to me that the only thing that would change would be that 0.20 would be changed to 0.40. That results in a negative value for x. What am I missing?
Thanks for any input.