Question

how much pure acid should be mixed with 6 gallons of a 50% acid solution in order to get a 70% acid solution? to get a 70% acid solution, you need □ gallon(s) of pure acid.

Explanation:

Step1: Set up an equation based on acid - content

Let $x$ be the number of gallons of pure acid (100% acid, or 1 in decimal form). The amount of acid in the 50% acid solution is $0.5\times6$ gallons, and the amount of acid in the pure - acid solution is $1\times x$ gallons. The total volume of the final solution is $(x + 6)$ gallons, and the desired concentration is 70% or 0.7. So the equation is $x+0.5\times6=0.7(x + 6)$.

Step2: Expand and simplify the equation

$x + 3=0.7x+4.2$.
Subtract $0.7x$ from both sides: $x-0.7x+3=0.7x - 0.7x+4.2$, which gives $0.3x+3 = 4.2$.

Step3: Solve for $x$

Subtract 3 from both sides: $0.3x+3 - 3=4.2 - 3$, so $0.3x=1.2$.
Divide both sides by 0.3: $x=\frac{1.2}{0.3}=4$.

Answer:

4