By Fatskills Exam Guides Team — the exam nerds behind 28,500+ quizzes and 2.1M practice questions across 500+ global exams.
Work and mixture problems involve finding the amount of a substance or quantity that results from combining different rates or proportions. This concept is essential in various fields, including chemistry, engineering, and economics, where understanding the outcomes of mixing different substances or rates is crucial.
Work and mixture problems have numerous real-world applications, such as: * Calculating the concentration of a solution by mixing different chemicals. * Determining the optimal mixture of ingredients for a product. * Understanding the impact of different interest rates on investments.
The following are the key foundational ideas and principles needed to understand work and mixture problems: * Combined Rates: The rate at which two or more substances are mixed together. * Alligation: A method for finding the proportion of a substance in a mixture by comparing the rates of the substances. * Mixture Problems: Problems involving the combination of different substances or rates to produce a desired outcome.
To solve work and mixture problems, follow these steps:1. Identify the problem: Clearly state the problem and the given information.2. Set up the equation: Use the formula for combined rates or alligation to set up an equation based on the given information.3. Solve for the unknown: Use algebraic methods to solve for the unknown quantity.4. Check your answer: Verify that the solution makes sense in the context of the problem.
A solution is made by mixing 2 liters of water with 3 liters of juice. If the mixture is to be 20% juice, how much more juice is needed?
Let x be the amount of juice needed. The total mixture will be 2 + x liters.
$$\frac{3}{2+x} = 0.2$$ $$3 = 0.2(2+x)$$ $$3 = 0.4 + 0.2x$$ $$2.6 = 0.2x$$ $$x = \frac{2.6}{0.2}$$ $$x = 13$$
13 liters of juice are needed.
The mixture will be 20% juice if 13 liters of juice are added to the 2 liters of water.
A mixture of 20% acid and 80% water is to be made by mixing 2 liters of 10% acid solution with 3 liters of 30% acid solution. How much acid is in the final mixture?
Let x be the amount of acid in the final mixture.
$$x = 0.2(2+3) + 0.1(2) + 0.3(3)$$ $$x = 1 + 0.2 + 0.9$$ $$x = 2.1$$
The final mixture contains 2.1 liters of acid.
The mixture will contain 20% acid if 2.1 liters of acid are present.
A) 10 liters B) 13 liters C) 15 liters D) 20 liters
B) 13 liters
The correct answer is 13 liters because the mixture will be 20% juice if 13 liters of juice are added to the 2 liters of water.
A) 10 liters is too little juice to achieve the desired concentration. C) 15 liters is too much juice and would result in a mixture that is too watery. D) 20 liters is the total amount of juice needed, not the additional amount needed.
A) 1 liter B) 2 liters C) 2.1 liters D) 3 liters
C) 2.1 liters
The correct answer is 2.1 liters because the final mixture will contain 20% acid if 2.1 liters of acid are present.
A) 1 liter is too little acid to achieve the desired concentration. B) 2 liters is the total amount of acid in the 10% solution, not the final amount in the mixture. D) 3 liters is the total amount of acid in the 30% solution, not the final amount in the mixture.
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