Question

One antifreeze solution is 37% alcohol and another is 16% alcohol. How much of each mixture should be added to make 42 L of a solution that is 28% alcohol?

____L of 37% solution should be mixed.

Answer 1

To make a 42-liter solution that is 28% alcohol, 24 liters of the 37% alcohol solution should be mixed with the 16% alcohol solution.

Step-by-step explanation:

To solve this problem, we can use a system of equations. Let x be the amount of the 37% alcohol solution and y be the amount of the 16% alcohol solution. We want to find the values of x and y such that the following two conditions are satisfied:

• The total volume is 42 liters: x + y = 42
• The final solution is 28% alcohol: 0.37x + 0.16y = 0.28(42)

We can solve this system of equations using substitution or elimination. Rewriting the first equation, we get y = 42 - x. Now, substituting this into the second equation gives us:

0.37x + 0.16(42 - x) = 11.76

Now we can solve for x:

0.37x + 6.72 - 0.16x = 11.76

0.21x = 5.04

x = 24 liters

So, 24 liters of the 37% solution should be mixed to achieve the desired concentration.