Answer:
To solve this problem, we can set up an equation based on the principle of the amount of acid:
Let's assume that "x" represents the amount of pure acid (100% concentration) that needs to be added to the mixture.
The equation can be set up as follows:
0.4 * 3 + 1 * x = 0.9 * (3 + x)
In this equation, the left side represents the total amount of acid in the initial mixture (3 gallons of 40% acid solution mixed with x gallons of pure acid), and the right side represents the desired amount of acid in the final mixture (90% acid solution).
Now, let's solve the equation:
0.4 * 3 + x = 0.9 * 3 + 0.9 * x
1.2 + x = 2.7 + 0.9x
Rearranging the equation:
x - 0.9x = 2.7 - 1.2
0.1x = 1.5
Dividing both sides by 0.1, we get:
x = 15
Therefore, you would need to mix 15 gallons of pure acid with 3 gallons of the 40% acid solution to obtain a 90% acid solution.