Question

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?

Answer 1

`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`