Answer:
84 pounds per square inch
Step-by-step explanation:
 Extracting the key information from the question:
*** Volume of a gas is inversely proportional to pressure of the gas.
*** A balloon is filled with  228 cubic inches of a gas at a pressure of 14 pounds per square inch.
*** Volume is then decreased to 38 cubic inches. we are required to find the new pressure of the gas.
  Since volume is inversely proportional to pressure, then:
   V = k × (1/p)
   V = k/p
V = volume, p= pressure, k = mathematical constant
Since, V = 228 cubic inches, P = 14 pounds per square inches, k = ?
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 Substituting appropriately, we have:
   228/1 = k/14
 cross multiply
K = 228 × 14 = 3192
 Using the same formula, we can calculate the new pressure of the gas since we know our mathematical constant and the volume it was decreased to.
 V = k/p
Here, volume = 38, k = 3192
 We now have:
  38/1 = 3192/p
 Cross multiply
 38 × p = 3192
  p = 3192/38
  p = 84 pounds per square inch.
 The new pressure of the gas after decrement of the volume= 84 pounds per square inch
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When the temperature stays the same, the new pressure of the gas if the volume is decreased is 84 pounds per square inch.
Given the following data:
To find the new pressure of the gas if the volume is decreased:
Translating the word problem into a mathematical expression, we have;
[tex]V \alpha \frac{1}{P} \\\\V = \frac{k}{P}[/tex]
Where:
First of all, we would determine the constant of proportionality.
[tex]k = VP\\\\k = 228 \times 14[/tex]
k = 3,192
To find the new pressure:
[tex]P = \frac{k}{V} \\\\P = \frac{3192}{38}[/tex]
New pressure, P = 84 pounds per square inch
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