I do not know how to set up this word problem?

Question

Your 10- gallon mixture currently consists of 70 percetn liquid A and 30 percent liquid B. How  much liquid B do you need to add to the mixture so that if will contain 42% liquid B?           Let x = liquid B      X+10 x .30    I reach this far and I am lost.

Answer 1

In a 10 gallon mixture, there are 7 gallons of A and 3 gallons of B.

If we add x gallons of B we will have 7+3+x=10+x gallons of mixture.

In those 10+x gallons there will be x+3 gallons of B so:

(x+3)/(10+x) is the proportion of B in the new mixture. We know this proportion is 42% or 0.42.

Therefore: (x+3)/(10+x)=0.42.

x+3=0.42(10+x)=4.2+0.42x,

x-0.42x=4.2-3=1.2,

0.58x=1.2,

x=1.2/0.58=2.069 gallons approximately.