What is a mixture in mathematical terms?

A mixture in mathematical terms refers to a combination of two or more different substances or quantities, where the overall characteristics depend on the proportions of the individual components. For example, mixing two solutions with different concentrations results in a new solution with a concentration that is a weighted average of the components.

What is the alligation method?

The alligation method is a technique used to determine the proportions of two or more components in a mixture based on their respective costs or concentrations. It involves setting up a simple calculation to find the ratio in which the components must be mixed to achieve a desired average.

If a mixture contains 30% Solution A and 70% Solution B, what is the average concentration of the mixture?

The average concentration of the mixture can be calculated as a weighted average: (0.30 * Concentration of A) + (0.70 * Concentration of B). If the exact concentrations of A and B are known, substitute those values to find the average concentration.

A solution contains 40% salt and another solution contains 20% salt. How many liters of each solution should be mixed to obtain 10 liters of a solution that is 30% salt?

Let x be the liters of the 40% solution and (10 - x) be the liters of the 20% solution. Set up the equation: 0.40x + 0.20(10 - x) = 0.30 * 10. Solving this gives x = 5 liters of the 40% solution and 5 liters of the 20% solution.

What is the formula for finding the average concentration in a mixture?

The average concentration C of a mixture can be calculated using the formula: C = (C1 * V1 + C2 * V2) / (V1 + V2), where C1 and C2 are the concentrations of the two components, and V1 and V2 are their respective volumes.

A fruit seller has two types of apples, one costing $2 per kg and the other costing $3 per kg. If he wants to create a mixture that costs $2.50 per kg, in what ratio should he mix the two types?

Using the alligation method, set up the differences: (3 - 2.5) = 0.5 for the $3 apples and (2.5 - 2) = 0.5 for the $2 apples. Hence, the ratio is 1:1.

If a mixture of two chemicals A and B costs $50 and $70 per liter respectively, how much of each chemical should be mixed to obtain 20 liters of a mixture costing $60 per liter?

Let x be the liters of chemical A and (20 - x) be the liters of chemical B. Set up the equation: 50x + 70(20 - x) = 60 * 20. Solving gives x = 10 liters of chemical A and 10 liters of chemical B.

A certain mixture contains 35% sugar and 65% water. If you need to prepare 200 ml of this mixture, how much sugar and how much water do you need?

To find the amounts, calculate: Sugar = 0.35 * 200 = 70 ml and Water = 0.65 * 200 = 130 ml.

What is the key principle behind using the alligation method?

The key principle of the alligation method is to determine the ratio in which two or more substances at different prices or concentrations should be mixed to achieve a desired average price or concentration.

If two solutions of different concentrations are mixed, how does the final concentration relate to the concentrations of the individual solutions?

The final concentration is a weighted average of the concentrations of the individual solutions, based on the volumes or proportions of each solution in the mixture.