How many liters of a 7% solution of salt should be added to a 27% solution in order to obtain 640 liters of a 12% solution?

2 Answers
Jun 14, 2018

Answer:

#160" Litres at 27%"#

#480" Litres at 7%"#

Explanation:

Let the volume of 7% solution be #S_7#

Let the volume of 27% solution be #S_(27)#

Let the target volume of 12% solution be #S_(12)=640#

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In this situation we have two separate condition that link the proportions.

Relationship by total volume: #->S_7+S_(27)=S_(12)=640#

By % content: #->[7/100xxS_7]+[27/100xxS_(27)]=12/100xx640#

Two unknowns and two equations. Thus solvable.

#S_7+S_(27)=640" "......................Equation(1)#

#(7S_7)/100+(27S_27)/100=384/5" ".............Equation(2)#
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#color(blue)("Determine the value of "S_(27))#

Consider #Eqn(2)#

#(7S_7+27S_27)/100=384/5#

Multiply both sides by 100

#7S_7+27S_(27)=7680" "....Equation(2_a)#

#Eqn(2_a)-7Eqn(1)#

#7S_7+27S_(27)=7680#
#ul(7S_7+color(white)(2)7S_(27)=4480larr" Subtract"#
#color(white)("d")0color(white)("d") +20S_(27)=3200#

Divide both sides by 20

#color(red)(S_(27)=160)#
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#color(blue)("Determine the value of "S_7)#

Substitute into #Eqn(1)#

#color(green)(S_7+color(red)(S_(27))=640 color(white)("dddd")->color(white)("dddd") S_7+color(red)(160)=640)#

#S_7=480#
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#color(blue)("Check")#

#[7/100xx480]+[27/100xx160]=12/100xx640#

#[ 33.6]+[43.2 ]=76.8#

#76.8=76.8# Thus correct

Jun 14, 2018

Answer:

Alternative and more efficient approach.

#480" Litres of 7% solution"#
#160" Litres of 27% solution"#

Explanation:

Let the volume of 7% solution be #S_7#

Let the volume of 27% solution be #S_(27)#

Let the target volume of 12% solution be #S_(12)=640#
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#color(red)(S_7=640-S_(27))#

Thus we have by percentage we have:

#color(green)(color(white)("dd")[7/100xxcolor(red)(S_7)]color(white)("ddddd")+[27/100xxS_(27)]=12/100xx640)#

By substitution for #S_7# we have:

#color(green)([7/100xx(color(red)(640-S_(27)))]+[27/100xxS_(27)]=12/100xx640)#

#44.8-(7S_27)/100+(27S_27)/100 = 76.8#

# (20S_(27))/100 =32#

#S_27=(32xx100)/20 = 160#
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Thus #S_7=640-160=480#