You have two beakers of acid solution. One beaker contains a 17% acid solution, and the other beaker contains a 91% ACID SOLUTION. How many liters of the 17% acid solution must you mix with the 91% acid solution to make 2 liters of a 56% acid solution? write the answer correct to two decimal places.
amount of 17% solution --- x L
amount of 91% solution --- 2-x L
.17x + .91(2-x) = .56(2)
solve for x
thank you for your help
.17x + 1.82 -.91x = 1.12
-.74x = -.7
x = -.7/-.74
x = .945
To solve this problem, we need to use the concept of mixture equations. Mixture equations allow us to find the quantity of different substances needed to create a desired mixture with specific concentrations.
Let's begin by assigning variables to the unknown quantities:
Let x be the number of liters of the 17% acid solution.
Then, (2 - x) represents the number of liters of the 91% acid solution.
Since we want to create a 2-liter mixture with a concentration of 56% acid solution, we can set up the following equation based on the acid content:
0.17x + 0.91(2 - x) = 0.56(2)
Let's solve for x using this equation:
0.17x + 1.82 - 0.91x = 1.12
Group like terms:
-0.74x = 1.12 - 1.82
-0.74x = -0.70
Solve for x by dividing both sides by -0.74:
x = -0.70 / -0.74
x ≈ 0.95
Therefore, you would need to mix approximately 0.95 liters of the 17% acid solution with (2 - 0.95) ≈ 1.05 liters of the 91% acid solution to create 2 liters of a 56% acid solution.