Solve the problem.
-A chemistry department wants to make 3 liters of a 17.5% basic solution by mixing a 20% solution with a 15% solution. How many liters of each type of basic solution should be used to produce the 17.5% solution?
A) 1 liter of 15% solution, 2 liters of 20% solution
B) 1.5 liters of 15% solution, 1.5 liters of 20% solution
C) 2 liters of 15% solution, 1 liter of 20% solution
D) 0.5 liter of 15% solution, 2.5 liters of 20% solution

Question

Quizplus · Accepted Answer

Let x be the liters of 15% solution and y be the liters of 20% solution. Then we have the system of equations:
x + y = 3 (because we want to make 3 liters of solution)
0.15x + 0.20y = 0.175(3) (because we want the final solution to be 17.5% basic)
Solving this system of equations gives x = 1.5 and y = 1.5, so we need 1.5 liters of each solution. Therefore, the best choice is B. We can use the following formula to solve this problem:

(amount of 15% solution)(percentage of 15% solution) + (amount of 20% solution)(percentage of 20% solution) = (amount of final solution)(percentage of final solution)

Let x be the amount of 15% solution and y be the amount of 20% solution. Then we have:

(x)(0.15) + (y)(0.20) = (3)(0.175)

0.15x + 0.20y = 0.525

Multiplying both sides by 100, we get:

15x + 20y = 52.5

Dividing both sides by 5, we get:

3x + 4y = 10.5

We want to solve for x and y, so we need another equation. We know that we need a total of 3 liters of solution, so:

x + y = 3

We can solve this system of equations by substitution or elimination. Here, we will use elimination:

3x + 4y = 10.5
x + y = 3

Multiplying the second equation by -3, we get:

-3x - 3y = -9

Adding this equation to the first one, we get:

3x + 4y = 10.5
-3x - 3y = -9
----------------
y = 1.5

Now we can use either equation to solve for x. Let's use the second one:

x + y = 3

x + 1.5 = 3

x = 1.5

Therefore, we need 1.5 liters of 15% solution and 1.5 liters of 20% solution to make 3 liters of 17.5% solution. So the best answer is B.

Solve the Problem. -A Chemistry Department Wants to Make 3 Liters of a Liters