Professor Baird wants to mix a solution containing 10% acid with one containing 15% acid to obtain a 20 ounce solution containing 12% acid. How many ounces of the 10% solution should the professor use?
Translate the word problem into an equation.
add up the amount of acid in each part:
.10x + .15(20-x) = .12(20)
x = 12
so, 12 oz 10% and 8 oz 15%
Let's assume the professor wants to use x ounces of the 10% acid solution.
The amount of acid in the 10% solution can be calculated as 0.10x.
Similarly, the amount of acid in the 15% solution would be 0.15(20 - x), since the professor is using a 20 ounce solution and has already used x ounces of the 10% solution.
To find the amount of acid in the final solution, we add the amounts from each solution: 0.10x + 0.15(20 - x).
Since the professor wants a 20 ounce solution containing 12% acid, we can set up the equation:
0.10x + 0.15(20 - x) = 0.12(20).
This equation represents the given information.
To solve this problem, let's first define our variables:
Let's call the number of ounces of the 10% acid solution that the professor should use as "x".
Now let's translate the information given in the problem into an equation:
The acid content in the 10% acid solution is 10%.
The acid content in the 15% acid solution is 15%.
The total volume of the final solution is 20 ounces.
The desired acid content in the final solution is 12%.
Using this information, we can set up the equation:
0.10x + 0.15(20 - x) = 0.12(20)
Explanation of the equation:
The left side of the equation represents the acid content in the original 10% acid solution and the acid content in the 15% acid solution, which are mixed together.
0.10x represents the acid content (in ounces) in the 10% solution that the professor is using.
0.15(20 - x) represents the acid content (in ounces) in the 15% solution that is used to make up the remaining part of the 20-ounce final solution.
The right side of the equation represents the desired acid content in the final solution.
0.12(20) represents the acid content (in ounces) that would be present in a 20-ounce solution with a 12% acid concentration.
Now, you can solve the equation for x to find the number of ounces of the 10% solution that the professor should use.