A solution of 54% alcohol is to be mixed with a solution of 22% alcohol to form 64 liters of a 42% solution. How many liters of the 54% solution must be used?

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Answer 1 · 2018-03-06T11:48:59

#40# liters of #54%# alcohal must be used.

Let #x# liters of #54%# alcohal is mixed with #(64-x) liters of

#22%# alcohal is mixed to get #64# liters of #42%# alcohal.

#:. x*0.54+(64-x)*0.22=64*0.42#

#:. 0.54x-0.22x=64*0.42-64*0.22# or

# 0.32x=64*(0.42-0.22)# or

# 0.32x=64*0.2 :. x =(64*0.2)/0.32# or

#x=40 :. 64-x= 64-40=24# liters. Hence #40# liters of #54%#

alcohal is mixed with #24# liters of #22%# alcohal is mixed to

get #64# liters of #42%# alcohal. [Ans]