Math Problem Statement
Björn took a poll for an upcoming local election and found that 27% of voters were likely to vote for the incumbent. His poll has a 4% margin of error.
Which of the following equations represents the likely minimum and maximum percentages of voters, v , that will vote for the incumbent?
Choose TWO correct answers A.|27−4|=v
B.|4−v|=27
C.|4−27|=v
D.|v−27|=4
E.|v−4|=27
F.|27−v|=4
Solution
In this problem, the margin of error tells us that the actual percentage of voters likely to vote for the incumbent could be as much as 4% higher or lower than the reported 27%. We need to find two equations that represent this situation.
Let's break it down:
-
Maximum likely percentage:
The highest percentage could be is %. -
Minimum likely percentage:
The lowest percentage could be is %.
The problem is asking for equations that express the relationship between and the given numbers, taking into account the margin of error.
Now, let's check the options:
-
Option A:
This simplifies to , or , which matches the minimum percentage. This is a correct option. -
Option B:
This equation does not logically represent the situation, as it suggests that the difference between 4 and is 27, which doesn't relate to the problem. This is not correct. -
Option C:
This simplifies to , or , which matches the minimum percentage, but it is redundant with Option A and does not cover the full range. This is not correct. -
Option D:
This represents the maximum percentage, since . This is a correct option. -
Option E:
This would imply , but this is not quite the right setup for the margin of error situation. This is not correct. -
Option F:
This represents the minimum percentage, since . This is a correct option.
Correct answers:
- A:
- D:
- F:
Do you have any questions or want more details?
Related questions:
- How is the margin of error typically calculated in polls?
- What is the meaning of the absolute value notation in real-life contexts?
- What would the result be if the margin of error increased to 5%?
- How do we handle rounding when dealing with percentages and polling?
- What other statistical factors affect the accuracy of poll results?
Tip: When working with percentages, always keep an eye on possible rounding errors, especially in large datasets.
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Math Problem Analysis
Mathematical Concepts
Algebra
Absolute Value
Linear Equations
Formulas
v = 27 ± 4
|27 - 4| = v
v - 27 = 4
27 - v = 4
Theorems
Absolute Value Properties
Linear Equation Solving
Suitable Grade Level
Grades 8-10
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