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# Let x be the amount of 70% chlorinated solution and y be the amount of 40% chlorinated solution.
# Then,0.7x + 0.4y = 0.55(x + y)
# 0.7x + 0.4y = 0.55x + 0.55y
# 0.3x = 0.15y
# x = 0.5y
# x + y = 200
# 0.5y + y = 200
# 1.5y = 200
# y = 200/1.5
# y = 133.33
# x = 0.5y
# x = 0.5(133.33)
# x = 66.67
# So, 66.67 gallons of 70% chlorinated solution and 133.33 gallons of 40% chlorinated solution are needed to make a 200-gallon solution that has 55% chlorine.