Two acid solutions are to be mixed together. Solution A is 30% acid by volume. Solution B is 70% acid by volume.
The 800 mL mixture is 54% acid by volume. The amount of Solution A, rounded to the nearest milliliter, is ____________mL.
.30A + .70(800-A) = .54(800)
To find the amount of Solution A, we can set up an equation using the information given.
Let's denote the amount of Solution A as x mL.
Based on the problem, we know that the total volume of the mixture is 800 mL and that the mixture is 54% acid by volume.
So, Solution A will contribute 30% of x mL acid to the mixture, which is 0.3x mL acid.
Solution B will contribute 70% of the remaining volume (800 - x) mL acid to the mixture, which is 0.7(800 - x) mL acid.
The total amount of acid in the mixture is the sum of the acids contributed by Solution A and Solution B. It is given as 54% of the total volume, which is 0.54 * 800 mL acid.
Setting up an equation using the information above, we have:
0.3x + 0.7(800 - x) = 0.54 * 800
Now, we can solve this equation to find the value of x, which is the amount of Solution A.
0.3x + 0.7(800 - x) = 0.54 * 800
0.3x + 560 - 0.7x = 432
0.4x = 432 - 560
0.4x = -128
x = -128 / 0.4
x = 320 mL (rounded to the nearest milliliter)
Therefore, the amount of Solution A, rounded to the nearest milliliter, is 320 mL.