Short Answer 
To create a 160-liter syrup mixture with a 20% concentration, you need to combine 160 liters of 10% syrup with 40 liters of 60% syrup. The calculation involves setting up an equation to balance the concentrations and solve for the required amounts of each syrup.
Step 1: Understand the Requirement
The task is to make a syrup mixture that consists of different concentrations. In this case, you need to create a total of 160 liters of syrup that has a concentration of 20%. To achieve this mixture, you will need to combine different volumes of syrups with varying concentrations, specifically 10% and 60% syrups.
Step 2: Set Up the Equation
To represent the relationship between the different syrup concentrations and their volumes, we need to set up an equation. Let x be the amount of 10% syrup used. We start by expressing the total amount of syrup from 60% and the 10% syrup resulting in the desired 20% solution:
- Calculate the contribution from 60% syrup: 0.6 * 40 liters
- Express the contribution of 10% syrup: x * 0.1 liters
- Create the equation for 20% solution: (x + 40) * 0.2 liters
Step 3: Solve for x and Conclude
Now, you’ll solve the equation to find the value of x. This involves rearranging the equation and isolating x:
- Combine the terms: 0.6 * 40 + 0.1x = 0.2x + 8
- Rearrange to find x: x = 160 liters
- Thus, to make the mixture, you need 160 liters of 10% syrup.