Mom made a 5% bleach solution with 50 ml of bleach and 950 ml water. How much bleach should be added to this in order to obtain a 15% bleach solution?

Question

Mateo Aguilar · Accepted Answer

#117.6# ml

The current solution has #50# ml of bleach and a total volume of #50+950 = 1000# ml. If we add a certain quantity #b# of bleach, we will have more bleach, but also more solution in general: the ratio bleach-to-total volume will change as follows: #\frac{50+b}{1000+b}# we want this ratio to equal #15% = 0.15#, so we must ask #\frac{50+b}{1000+b} = 0.15# Solve for #b#: if we multiply both sides by #1000+b# we have #50+b = 0.15(1000+b) = 150+0.15b# Subtract #0.15b# from both sides: #50+b-0.15b = 150# Subtract #50# from both sides: #b-0.15b = 150 - 50# Make both sides simple: #0.85b = 100# Divide both sides by #0.85# #b = \frac{100}{0.85} \approx 117.6# Let's check our answer: the new solution will have #50+117.6 = 167.6# ml of bleach, for a total volume of #1000+117.6 = 1117.6# ml. The ratio is #\frac{167.6}{1117.6} \approx 0.15# so everything is well!

Naomi Aronson · Answer

undefined To obtain a 15% bleach solution, an additional 300 ml of bleach should be added.