12. The volume V of a gas varies inversely with the pressure P. When the volume is 75 inches cubed, the pressure is 30 pounds per square inch. What is the volume when the pressure is 25 pounds per square inch?

Let V = the gas' volume and P = its pressure.  The volume of a gas in a container varies inversely with the pressure on the gas:

    V = k/P

where  k is a constant.  To find the value of k, plug in the one known point, V = 390 cubic inches when P = 7 pounds per square inch and solve for k:

    V = k/p

    390 = k/7

    390*7 = k

    2730 = k

The full equation, then, is:

    V = 2730/P

To find the volume when P = 9 pounds per square inch:

    V = 2730/9 = cubic inches

Step-by-step explanation:

Let V = the gas' volume and P = its pressure.  The volume of a gas in a container varies inversely with the pressure on the gas:

    V = k/P

where  k is a constant.  To find the value of k, plug in the one known point, V = 390 cubic inches when P = 7 pounds per square inch and solve for k:

    V = k/p

    390 = k/7

    390*7 = k

    2730 = k

The full equation, then, is:

    V = 2730/P

To find the volume when P = 9 pounds per square inch:

    V = 2730/9 = cubic inches

translate k to n and reflect across the line containing jk.