Question 126591
The two key words in this exercise are "directly" and "inversely".
--If one variable varies directly with another it increases or decreases as the other increases or decreases. (move in the same direction)
--If one variable varies inversely as another it decreases as the other increases and increases as the other decreases. (move in opposite directions)

To translate this algebraically:
A. "Volume V varies directly as the Temperature T"  = {{{V/T}}} or divide
B. "Volume V varies inversely as the Pressure P" = {{{V*P}}} or multiply

Putting this all together:
{{{P*V/T}}}

1. Table of values
Let V1 = 465
Let P1 = 10
Let T1 = 310

Let P2 = 20
Let T2 = 300
2. Find V2

3.{{{P*V/T = P1*V1/T1 = P2*V2/T2}}} Set up a proportion:
4.{{{P*V/T = 10*465/310 = 20*V2/300}}} Substitute the given values
5.{{{P*V/T = 15 = 20*V2/300}}} Solve for V2
6.{{{4500 = 20*V2}}} Cross-multiply
7.{{{V2 = 225}}}
8. Check your answer
{{{10*465/310 = 15}}}
{{{20*225/300 = 15}}}
{{{15 = 15}}}
The answer is correct.