2. Regla de Tres
1. Un juez tarda 4 horas en revisar 12 expedientes. ¿Cuánto tarda para 46?
$-\frac{4}{12}=\frac{x}{46} \Rightarrow$
Answer (2)
Set up a proportion: 12 4 = 46 x .
Solve for x : x = 12 4 × 46 .
Calculate x : x = 12 184 = 15.333... .
The time it takes to review 46 files is approximately 15.33 hours.
Explanation
Understanding the Problem Let's analyze the problem. We know that a judge takes 4 hours to review 12 files. We need to find out how many hours it will take the judge to review 46 files, assuming the judge works at the same rate. We can set up a proportion to solve this problem.
Setting up the Proportion We can set up a proportion where the ratio of time to files is constant. Let x be the time it takes to review 46 files. The proportion is: files time = 12 4 = 46 x
Solving for x Now, we solve for x by multiplying both sides of the equation by 46: x = 12 4 × 46
Calculating the Value of x Now, we perform the calculation: x = 12 4 × 46 = 12 184 = 3 46 = 15.333... So, it will take approximately 15.33 hours to review 46 files.
Final Answer Therefore, it will take the judge approximately 15.33 hours to review 46 files.
Examples
Understanding proportions is useful in many real-life situations. For example, if you know the price of one item, you can use a proportion to find the price of multiple items. If one apple costs 0.50 , yo u c an se t u p a p ro p or t i o n t o f in d t h ecos t o f 10 a ppl es : \frac{1}{0.50} = \frac{10}{x} . S o l v in g f or x g i v es x = 5$, so 10 apples would cost $5. Proportions are also used in cooking, scaling recipes, and converting units.
To find how long it takes for a judge to review 46 files, we use proportions. Solving the ratio of 4 hours for 12 files, we find that it takes approximately 15.33 hours for 46 files. This demonstrates the use of the Rule of Three in solving proportional problems.
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