How do you solve weighted averages where you are trying to take, let's say, 80% solution that has 20 gallons, and add it to x amount of 30% solution to make 50% solution?
Start with 'x'
Say that is the amount of 30% solution you need to add .3x
then the final volume will be 20 gallons PLUS x or 20 + x
this new, bigger volume is to be 50% or .5 (20+x)
the two sides of the equation have to equal : what you started with plus what you added have to equal the final solution
you started with .8(20) and added .3x
so
.8(20) + .3x has to equal .5 (20+x)
.8 (20) +.3x = .5 (20+x)
16 + .3x = 10 + .5x solve for 'x'
6 = .2x
x = 30 gallons of 30% solution
Start with 'x'
Say that is the amount of 30% solution you need to add .3x
then the final volume will be 20 gallons PLUS x or 20 + x
this new, bigger volume is to be 50% or .5 (20+x)
the two sides of the equation have to equal : what you started with plus what you added have to equal the final solution
you started with .8(20) and added .3x
so
.8(20) + .3x has to equal .5 (20+x)
.8 (20) +.3x = .5 (20+x)
16 + .3x = 10 + .5x solve for 'x'
6 = .2x
x = 30 gallons of 30% solution
