Problem:
How many liters of a 35% sugar solution should be added to a 17% sugar solution to obtain 72 liters of a 25% sugar solution?

Solution:
To solve this problem, we can use the concept of mixtures. Let's break down the solution into steps:

Step 1: Define the variables:
Let's denote the amount of 35% sugar solution to be added as x liters.

Step 2: Set up the equation:
We need to find the amount of sugar in the resulting solution. The equation can be set up as follows:

Total sugar in the 35% solution + Total sugar in the 17% solution = Total sugar in the 25% solution

(0.35x) + (0.17(72 - x)) = 0.25(72)

Step 3: Solve the equation:
Simplifying the equation, we have:

0.35x + 0.17(72 - x) = 18

0.35x + 12.24 - 0.17x = 18

0.18x + 12.24 = 18

0.18x = 5.76

x = 5.76 / 0.18

x ≈ 32

Therefore, we need to add approximately 32 liters of the 35% sugar solution to obtain 72 liters of the 25% sugar solution.

Explanation:
To understand why this solution works, let's consider the sugar content in each solution.

The 35% sugar solution contains 35 parts sugar and 65 parts solvent (water or any other liquid).

The 17% sugar solution contains 17 parts sugar and 83 parts solvent.

When we mix the two solutions, we are essentially combining the sugar content and the solvent content.

In the resulting 25% sugar solution, we want the ratio of sugar to solvent to be 1:3 (25 parts sugar and 75 parts solvent).

By setting up the equation and solving for x, we are finding the amount of the 35% sugar solution needed to achieve this desired ratio.

Adding 32 liters of the 35% sugar solution to 40 liters of the 17% sugar solution (72 - 32) will give us a total volume of 72 liters.

The sugar content in the resulting solution can be calculated as follows:

Total sugar = (0.35 * 32) + (0.17 * 40) = 11.2 + 6.8 = 18 g

The concentration of the resulting solution can be calculated as:

Concentration = (Total sugar / Total volume) * 100 = (18 / 72) * 100 ≈ 25%

Hence, by adding 32 liters of the 35% sugar solution to 40 liters of the 17% sugar solution, we obtain 72 liters of a 25% sugar solution.