How many liters of a 60% sugar solution should be added to 40 liters of a 30% sugar solution to produce a 50% sugar solution?

1 Answer
Jun 12, 2018

Answer:

#80" litres"#

Explanation:

Let the amount of 60% solution be #S_60#
Let the amount of 30% solution be #S_(30)=40" litres"#
Let the amount of 50% solution be #S_(50) =40+S_(60)" litres"#

So for this to balance we have:

#60/100S_(60)+(30/100xxS_(30))=50/100color(white)("d")S_(50)#

#60/100S_(60)+(30/100xx40)=50/100(S_(60)+40)#

#3/5S_(60) +12=1/2S_(60)+20 #

#3/5S_(60)-1/2S_(60)=20-12#

#1/10S_(60) = 8#

#S_(60) = 80" litres"#
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Check:

#(60/100xx80)+(30/100xx40)=48+12=60# of solute

#60/(40+80)xx100%=50%color(brown)(larr"Answer confimed"#

Note that #%# is a unit of measurement that is worth #1/100#
Consequently you are doing the equivalent of multiplying by 1 when you write: #xx100% -> 100xx1/100=100/100 = 1#