a 5% acid solution is mixed with a 9% acid solution. How many ounces of each solution are needed to obtain 40 ounces of a 6% solution?
the amount of acid in each part must total the acid in the mixture, so
.05x + .09(40-x) = .06(40)
Now just solve for x, the amount of 5% acid.
To solve this problem, we can use the method of mixture.
Let's assume that x ounces of the 5% acid solution are mixed with (40 - x) ounces of the 9% acid solution. The total solution will be 40 ounces, as mentioned.
Since the concentration of the acid is measured as a percentage, we can convert it to a decimal by dividing by 100. So, 5% is equivalent to 0.05, and 9% is equivalent to 0.09.
To find the concentration of the final mixture, we can sum up the products of the amount of each solution and its respective concentration, and then divide it by the total amount of the mixture.
Let's set up the equation:
0.05x + 0.09(40 - x) = 0.06 * 40
Now, we can solve for x:
0.05x + 3.6 - 0.09x = 2.4
-0.04x = -1.2
x = -1.2 / -0.04
x = 30
Therefore, 30 ounces of the 5% acid solution need to be mixed with (40 - 30) = 10 ounces of the 9% acid solution to obtain 40 ounces of a 6% solution.