a lab technician has a 15% alcohol solution. She wants to make 100 gallons of a 29% solution. How much of the 15% solution should she use?
To determine how much of the 15% alcohol solution the lab technician should use, we can set up the following equation based on the given information:
(amount of 15% solution) * 0.15 = (amount of alcohol in the solution)
Since the technician wants to make 100 gallons of a 29% solution, we can set up another equation using the same concept:
(amount of 29% solution) * 0.29 = (amount of alcohol in the solution)
We need to find the amount of the 15% solution, so let's call it "x". We know that the amount of the 15% solution should equal the amount of the 29% solution made, so we can set up an equation using these variables:
x = (amount of 29% solution)
Now, we can substitute the amounts of alcohol in the two equations with their corresponding expressions:
0.15x = 0.29 * 100
Simplifying the equation:
0.15x = 29
To solve for "x", divide both sides of the equation by 0.15:
x = 29 / 0.15
x ≈ 193.33
Therefore, the lab technician should use approximately 193.33 gallons of the 15% solution to make 100 gallons of a 29% solution.