Adding acid?

Question

How much pure acid should be mixed with 7 gallons of a 50% acid solution in order to get a 70% acid solution? 

Answer 1

.5×7 + x = the acid in the final soloution

7+x is the amount of the final solution

(3.5+x)/(7+x)=.7

3.5+x=.7(7+x)

3.5+x=4.9+.7x

.3x=1.4

x=14/3=4 2/3 gal

Note:3 1/2 + 4 2/3 = 8  1/6  total acid after addition of acid

7+4 2/3 = 11 2/3 gal total of final mixture

(8 1/6)/(11 2/3)=(49/6)/(70/6)=.7

Answer 2

7 gallons of a 50% solution contains 3.5 gallons of acid and water.  Let x = amt of pure acid added, then we set up the equation to calculate the percentage:

 

(3.5+x)/(7+x) = .70/1   Cross multiply and solve

 

.70(7+x) = (3.5+x)

 

4.9 + .7x = 3.5 + x

 

1.4 = .3x

 

x = 4.67 gallons of pure acid