Ideal Gas Law - Differential Approximation due to variable increase in %.

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The discussion centers on using the ideal gas law, P=kT/V, to approximate the percentage change in pressure due to a 3% increase in temperature and a 5% increase in volume. The original poster calculated a 2% change in pressure, while an online solution indicated a 4% change, leading to confusion about the discrepancy. The poster suspects a misunderstanding related to a division by 1/2 in the online solution. Clarification is sought on the logic behind this division and the correct application of differentials in the problem. Understanding the differential approximation is crucial for accurately determining the percentage change in pressure.
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Homework Statement


This is a problem form my calculus book, which states:

According to the ideal gas law, the pressure, temperature, and volume of a confined gas are related by P=kT/V, where K is a constant. Use differentials to approximate the percentage change in pressure if the temperature of a gas is increased 3% and the volume is increased 5%.

The Attempt at a Solution



Here, I include my original attempt at the solution and a solution that I found online. In my original solution, I found the answer to be 2%, but the solution says 4%. I'm not sure why... but I think it's related to something I don't understand in the actual solution, where it seems to me, they divide by 1/2 for no apparent logical reason.

Could someone please explain to me where my logic is flawed?
attachment.php?attachmentid=40470&d=1319929174.jpg


Here is a solution I found online to the same problem, perhaps it's more clear.
attachment.php?attachmentid=40468&d=1319927946.jpg
 

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Edited to make images easier to see. (Sorry.)
 

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