How many gallons of 5% acid solution should be mixed with 20 galllons of a 10% acid solution to obtain an 8% acid solution
let the amount of the 5% solution that must be added be x gallons
.05x + .10(20) = .08(20+x)
times 100
5x + 10(20) = 8(20+x)
5x + 200 = 160 + 8x
-3x = -40
x = 40/3
they should add 13 1/3 gallons of the 5% solution.
To determine the number of gallons of 5% acid solution needed, we can use the following formula:
(amount of 5% solution * percentage of acid in the 5% solution) + (amount of 10% solution * percentage of acid in the 10% solution) = (total amount of mixture * desired percentage of acid)
Let's solve the equation step-by-step.
Let x be the number of gallons of the 5% acid solution.
(amount of 5% solution * 5%) + (20 gallons * 10%) = (x + 20 gallons) * 8%
(0.05x) + (2 gallons) = (0.08x + 1.6 gallons)
Now, we can simplify the equation:
0.05x + 2 = 0.08x + 1.6
Subtracting 0.05x from both sides, we get:
2 = 0.08x - 0.05x + 1.6
0.03x = 0.4
Dividing both sides by 0.03, we find:
x = 0.4 / 0.03
x ≈ 13.333
Therefore, we need approximately 13.333 gallons of the 5% acid solution to obtain an 8% acid solution when mixed with 20 gallons of a 10% acid solution.
To solve this problem, we can use the concept of the mixture equation. The mixture equation states that the amount of acid in a mixture is equal to the sum of the amounts of acid in the individual components.
Let's denote the unknown amount of 5% acid solution we need to mix with 'x' gallons.
The amount of acid in the 20 gallons of 10% solution is 20 * 0.10 = 2 gallons.
The amount of acid in the 'x' gallons of 5% solution is x * 0.05 = 0.05x gallons.
The total amount of acid in the mixture is the sum of the above two quantities:
2 + 0.05x
According to the problem, we want the resulting mixture to be an 8% acid solution. So, the total amount of acid in the mixture should be 8% of the total volume of the mixture.
We have a total volume of 20 + x gallons. Therefore, the amount of acid in the mixture is (20 + x) * 0.08 = 1.6 + 0.08x gallons.
Now, we can set up an equation:
2 + 0.05x = 1.6 + 0.08x
To solve for 'x', we can subtract 0.05x from both sides:
2 - 1.6 = 0.08x - 0.05x
0.4 = 0.03x
Divide both sides by 0.03 to solve for 'x':
0.4 / 0.03 = x
x ≈ 13.33
Therefore, we need to mix approximately 13.33 gallons of 5% acid solution with 20 gallons of 10% acid solution to obtain an 8% acid solution.