Question 258411
You have 1 gallon of solution that is 20% salt and 80% water. You need 8 gallons of solution that is 2% salt and 98% water. How much water do you add to obtain this?

1 gallon = 128 oz
0.20*128=25.6 oz salt  (salt amount will not change)

0.02*(128+x)=25.6
2.56+0.02x=25.6
0.02x=23.04
x=1152 oz or 1152/128=9 gallons of water to be added

but this gives 10 gallons of prepared solution, and we wanted 8 gallons

0.8*128=102.4 oz of original solution
.20*102.4=20.48 oz salt (salt amount will not change)

0.02*(102.4+x)=20.48
2.048+0.02x=20.48
0.02x=18.432
x=921.6 oz or 921.6/128=7.2 gallons of water to be added
0.8 gallons original + 7.2 gallons of water = 8 gallons of prepared solution

so solution is either use 0.8 gallons of the original and prepare the 8 gallons
or use all of the original and have an extra 2 gallons of the prepared