Question

a.) How many gallons of a 30% salt solution must be added to 40 gallons of a 12% salt solution to obtain a 20% solution ?

b.) How much water should be added to one gallon of pure acid to obtain a 15% solution ?

Answer 1

a)

Let us consider that,

x = the no. gallons of a 30% salt solution that must be mixed with 40 gallons of a 12% solution to obtain a solution that is 20% solution so that,
0.3x + 40(0.12) = 0.2(40 + x)
0.3x + 4.8 = 8+ 0.2x
0.1x = 3.2
x = 32
Hence 32 gallons of a 30% salt solution must be added to 40 gallons of a 12% salt solution to obtain a 20% solution

b)

Here as per the given data we have,

1*1=0.15*(1+x)

1=0.15+0.15*x

1-0.15=0.15*x

0.85=0.15*x
x=17/3 gallons = 5.66666667 gallons

Hence 5.667 gallons of water should be added to one gallon of pure acid to obtain a 15% solution