MHB How to Correctly Express Percentage

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To determine the percentage difference in electricity usage between Nic and Linda, the correct calculation shows that Linda uses approximately 26% more electricity than Nic. This is derived by taking the difference in their usage (16211 kWh) and dividing it by Nic's usage (62425 kWh). If the question were framed as "what percent less does Nic use than Linda," the calculation would yield that Nic uses about 21% less than Linda. The base for percentage calculations is crucial, as it determines the reference point for comparison. Understanding these calculations is essential for accurately expressing percentage differences.
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I don't know how to express this: If Nic uses 62425 kwh of electricity and Linda uses 78636, does Linda use 20.6% more? How would this difference be correctly expressed as a percentage? Thanks!
 
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Hello and welcome to MHB, Linda!

If we let $P$ be the percentage in question, I would write:

$$P=\frac{78636-62425}{62425}\cdot100\%=\frac{64844}{2497}\%\approx25.9688\%$$
 
The percentage difference is the difference divided by the "base"
Here the difference is 78636- 62425= 16211.

Since this problem said "what percent more", the base is the smaller number, 62425.
\frac{16211}{62425}= 0.259 or 26%. Linda uses 26% more than Nic.

If the problem had said "What percent less does Nic use than Linda", the base would be the larger number, so we would calculate \frac{16211}{78636}= 0.21 or 21%. Nic uses 21% less than Linda.
 

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