Find the range of allowable values based on a measure of 130 inches if the values can vary by 1.4%.
Understand the Problem
The question is asking to find the range of values that can vary from a given measurement of 130 inches by 1.4%. This will involve calculating 1.4% of 130 and then determining the minimum and maximum allowable values.
Answer
The range of allowable values is $[128.18, 131.82]$ inches.
Answer for screen readers
The range of allowable values is $[128.18, 131.82]$ inches.
Steps to Solve
- Calculate 1.4% of 130 inches
To find the allowable variation, first calculate $1.4%$ of $130$ inches.
$$ 0.014 \times 130 = 1.82 \text{ inches} $$
- Determine the minimum allowable value
Subtract the calculated variation from the original measurement to find the minimum allowable value.
$$ 130 - 1.82 = 128.18 \text{ inches} $$
- Determine the maximum allowable value
Add the calculated variation to the original measurement to find the maximum allowable value.
$$ 130 + 1.82 = 131.82 \text{ inches} $$
- State the range of allowable values
The range of allowable values is from the minimum to the maximum value calculated.
$$ \text{Range} = [128.18, 131.82] \text{ inches} $$
The range of allowable values is $[128.18, 131.82]$ inches.
More Information
This range represents the acceptable variation around the original measurement of 130 inches, indicating how much it can fluctuate without going beyond the specified limit of 1.4%.
Tips
- Forgetting to convert the percentage to a decimal form before calculation. Always divide the percentage by 100, as in $1.4% = 0.014$.
- Not correctly applying addition and subtraction to find the minimum and maximum values.
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