How many liters of water must be added to 30 liters of a 10% brine solution to dilute it to an 8% solution?

Question

The answer is 7.5 liters, but I don't know how they got it. The formula for these types of problems is rb = a, where r is the rate, b is the base, and a is the amount. 

Answer 1

The easiest way to do this is by using V1C1 = V2C2

V1 = volume 1

C1 = concentration 1

V2 = volume 2

C2 = concentration 2

Thus, you have (30 liters)(10%) = (x liters)(8%)

x = 37.5 liters which means that the FINAL volume will be 37.5 liters.

Since you started with 30 liters, that mean that 7.5 liters of water must be added.

Answer 2

10% of 30=0.1*30=3 liters of brine are in the solution

let x=# of liters of water to be added

amount of brine/total amount of solution=% of brine solution

3/(30+x)=8%

3/(30+x)=8/100

cross multiply

3*100=8*(30+x)

300=240+8x

300-240=8x

60=8x

x=60/8

x=7 4/8

x=7 1/2

x=7.5 liters