Question

Suppose that you have a supply of a 40% solution of alcohol and a 60% solution of alcohol. how many quarts of each should be mixed to produce 100 quarts that is 50% alcohol?

Answer 1

To produce 100 quarts of a 50% alcohol solution, you will need 50 quarts of the 40% alcohol solution and 50 quarts of the 60% alcohol solution. This can be determined by solving a system of equations representing the total volume and alcohol content of the mixture.

Step-by-step explanation:

To find out how many quarts of each solution should be mixed to produce 100 quarts that is 50% alcohol, we can use a mixture problem. Let's assign variables to the unknown quantities:

x = quarts of 40% solution

y = quarts of 60% solution

The total volume of the mixture is 100 quarts, so we have the equation:

x + y = 100

The total amount of alcohol in the mixture is 50% of 100 quarts, so we have the equation:

0.40x + 0.60y = 0.50 * 100

Simplifying the second equation gives us:

0.40x + 0.60y = 50

Now we can solve the system of equations to find the values of x and y.

We can multiply the first equation by 0.40:

0.40x + 0.40y = 40

Subtracting this equation from the second equation eliminates the x variable:

0.60y - 0.40y = 50 - 40

0.20y = 10

Dividing both sides of the equation by 0.20 gives us:

y = 50

Substituting this value of y back into the first equation, we can solve for x:

x + 50 = 100

x = 50

Therefore, you need 50 quarts of the 40% solution and 50 quarts of the 60% solution to produce 100 quarts that is 50% alcohol.

Answer 2

50 quarts of 60% solution and 50 quarts of 40% solution. You want a total of 100 quarts, so we'll use the following expressions x = amount of 60% solution (100 - x) = amount of 40% solution. The total amount of alcohol will be 0.6x + 0.4(100-x) We want the final result to be 100 quarts of 50% solution, so we express that as 0.5 * 100 Now we set them equal to each other, and solve for x 0.6x + 0.4(100-x) = 0.5 * 100 Distribute the .4 0.6x + 0.4*100 - 0.4x = 0.5 * 100 0.6x + 40 - 0.4x = 50 Subtract 40 from both sides and combine the x terms 0.2x = 10 Divide both sides by 0.2 x = 50 Now we know we need 50 quarts of the 60% solution. And we need (100 - 50) = 50 quarts of the 40% solution as well.