You add x ml of a 25% alcohol solution to a 200 ml of a 10% alcohol solution to obtain another solution. Find the amount of alcohol in the final solution in terms of x. Find the ratio, in terms of x, of the alcohol in the final solution to the total amount of the solution. What do you think will happen if x is very large? Find x so that the final solution has a percentage of 15%.
Choose the correct option.
A) 100 ml B) 200 ml C) 300 ml D) 400 ml E) 500 ml
Let us first find the amount of alcohol in the 10% solution of 200 ml.   200 * 10% = 20 ml   The amount of alcohol in the x ml of 25% solution is given by   25% x = 0.25 x   The total amount of alcohol in the final solution is given by   20 + 0.25 x   The ratio of alcohol in the final solution to the total amount of the solution is given by   [ ( 20 + 0.25 x ) / (x + 200)]   If x becomes very large in the above formula for the ratio, then the ratio becomes close to 0.25 or 25% (The above function is a rational function and 0.25 is its horizontal asymptote). This means that if you increase the amount x of the 25% solution, this will dominate and the final solution will be very close to a 25% solution.   To have a percentage of 15%, we need to have   [ ( 20 + 0.25 x ) / (x + 200)] = 15% = 0.15   Solve the above equation for x   20 + 0.25 x = 0.15 * (x + 200)   x = 100 ml   100 mlnswer 100 ml
<result>A</result>
You add x ml of a 25% alcohol solution to a 200 ml of a 10% alcohol solution to obtain another solution. Find the amount of alcohol in the final solution in terms of x. Find the ratio, in terms of x, of the alcohol in the final solution to the total amount of the solution. What do you think will happen if x is very large? Find x so that the final solution has a percentage of 15%.