How much pure acid should be mixed with 3 gallons of a 50% acid solution in order to get an
80% acid solution?
The %'s always throw me off.
i got 4.5. Did i do that right?
.80(P+3)=P+.5(3) that is
end acid=sum of acids...
solve for P
To solve this problem, we can set up an equation based on the amount of acid present in the solution.
Let's assume that "x" gallons of pure acid need to be mixed with the 50% acid solution.
Step 1: Convert the percentages to decimals.
- The 50% acid solution can be written as 0.50 (50/100 = 0.50).
- The desired 80% acid solution can be written as 0.80 (80/100 = 0.80).
Step 2: Set up the equation.
The equation can be written as:
(0.50 * 3) + (1.00 * x) = (0.80 * (3 + x))
Explanation: We need to account for the amount of acid in both the 50% solution and the pure acid added. The left side of the equation represents the amount of acid in the initial solution (3 gallons of 50% acid) and the added pure acid (x gallons). The right side represents the amount of acid in the final solution (3 + x gallons of 80% acid).
Step 3: Simplify and solve the equation.
Multiply the percentages by their respective quantities:
1.50 + x = 2.40 + 0.80x
Combine like terms:
x - 0.80x = 2.40 - 1.50
0.20x = 0.90
Divide both sides by 0.20:
x = 0.90 / 0.20
x = 4.5
Therefore, 4.5 gallons of pure acid should be mixed with 3 gallons of a 50% acid solution to obtain an 80% acid solution.
To find the amount of pure acid that needs to be mixed with the 50% acid solution to get an 80% acid solution, we can follow these steps:
Step 1: Convert the given percentages to decimal form.
The 50% acid solution means that 50% of the solution is acid, which is equivalent to 0.50 (since 50% = 50/100 = 0.50).
Similarly, the 80% acid solution means that 80% of the solution is acid, which is equivalent to 0.80.
Step 2: Set up the equation.
Let's assume that x represents the amount of pure acid (in gallons) to be mixed.
The total volume of the new solution will be the sum of the initial 3 gallons and x gallons of pure acid, which is (3 + x) gallons.
The equation can be set up based on the acid content in the new solution:
0.50 * 3 + 1.00 * x = 0.80 * (3 + x)
In this equation, 0.50 * 3 represents the amount of acid in the 50% solution that is initially present, and 1.00 * x represents the amount of pure acid being added. The right side of the equation represents the desired acid content in the final solution.
Step 3: Solve the equation for x.
Let's solve the equation using the steps below:
0.50 * 3 + 1.00 * x = 0.80 * (3 + x)
1.5 + x = 2.4 + 0.8x (distribute 0.80 to the terms inside parentheses)
x - 0.8x = 2.4 - 1.5 (subtract x from both sides, subtract 1.5 from 2.4)
0.2x = 0.9 (0.2x = 0.9 after simplifying the equation)
x = 0.9 / 0.2 (divide both sides by 0.2)
x = 4.5
Therefore, you will need to mix 4.5 gallons of pure acid with the 3 gallons of 50% acid solution to obtain an 80% acid solution.