A chemistry teacher needs 2.5 liters of a sulfuric acid solution that is 20% sulfuric acid and 80% water . He has 2 liters of a 15% sulfuric acid solutionleft over from earlier laboratory exercises. He also has 44 liters of a 50% solution. Let x represent the number of liters of the 15% solution that can be mixed with Y liters of the 50% solution to make 2.5 liters of the needed 20% solution. Which of the following shows a system of equations that could get the solved to find the amounts of the 15% and 50% solutions that could be mixed to get the required solution?

Question

A chemistry teacher needs 2.5 liters of a sulfuric acid solution that is 20% sulfuric acid and 80% water . He has 2 liters of a 15% sulfuric acid solutionleft over from earlier laboratory exercises. He also has 44 liters of a 50% solution. Let x represent the number of liters of the 15% solution that can be mixed with Y liters of the 50% solution to make 2.5 liters of the needed 20% solution. Which of the following shows a system of equations that could get the solved to find the amounts of the 15% and 50% solutions that could be mixed to get the required solution?

A) X+Y=2.5
0.15X+0.50Y=0.20

B) x+y=0.20(2.5)
0.15x+0.50y=2.5

C) x+y=2.5
0.15x+0.50y=0.20(2.5)

D)x+y=0.65
x+y=0.20(2.5)

Answer 1

Please check if division signs are missing in some of the answers.

What is your choice, and why?

Answer 2

The correct answer is option C) x+y=2.5 and 0.15x+0.50y=0.20(2.5).

To solve this problem, we can set up a system of equations that represents the given information:

Let x represent the number of liters of the 15% solution.
Let y represent the number of liters of the 50% solution.

We know that the chemistry teacher needs a total of 2.5 liters of the 20% solution. So the first equation would be x+y=2.5.

We also know that the 20% solution is made up of 20% sulfuric acid and 80% water. The 15% solution contains 15% sulfuric acid, and the 50% solution contains 50% sulfuric acid. So we can represent this information in the second equation as follows: 0.15x+0.50y=0.20(2.5).

Thus, the correct system of equations to solve for x and y is x+y=2.5 and 0.15x+0.50y=0.20(2.5).

Answer 3

To solve this problem, we need to set up a system of equations using the given information.

Let's start by setting up the equation for the total amount of solution needed:
x + y = 2.5

Next, let's set up the equation for the concentration of sulfuric acid in the final solution. We can do this by adding up the amount of sulfuric acid from each solution and dividing it by the total volume of the solution (2.5 liters):
(0.15x + 0.50y) / 2.5 = 0.20

Now, let's review each option to determine which one correctly represents the system of equations:

A) X+Y=2.5
0.15X+0.50Y=0.20

This option correctly represents the system of equations, so it could be the solution.

B) x+y=0.20(2.5)
0.15x+0.50y=2.5

This option does not correctly represent the system of equations because it does not divide the concentration equation by the total volume of the solution.

C) x+y=2.5
0.15x+0.50y=0.20(2.5)

This option correctly represents the system of equations, so it could be the solution.

D) x+y=0.65
x+y=0.20(2.5)

This option does not correctly represent the system of equations because the left-hand side of the second equation is missing the concentration equation.

So, the possible correct answers are options A) and C).