How much pure acid should be mixed with 3 gallons of a 40% acid solution in order to get a 90% acid solution

Question

I have tried to solve this using a table but cannot seem to find the correct answer.

Answer 1

3 gallons of a 40% acid solution means you have 40%*3=1.2 gallons of acid already

let x=# of gallons of pure acid to be added to get a 90% acid solution

(1.2+x)/(3+x)=90%

(1.2+x)/(3+x)=9/10

cross multiply

10(1.2+x)=9(3+x)

12+10x=27+9x

10x-9x=27-12

x=15 gallons of pure acid must be added

check: 3+15=18 gallons of which (1.2+15) 16.2 gallons are pure acid

16.2/18=162/180=54/60=9/10=90/100=90%