Algebraic Word Problem

Question

The volume, V, of a certain gas varies inversely with the amount of pressure, P, placed on it. The volume of this gas is 175 cm^3 when 3.2 kg/cm^2 of pressure is placed on it. What amount of pressure must be placed on 400cm^3 of this gas?

Answer 1

Accidentally deleted my first response while writing an edit so here it is again:

And inverse relationship looks like the below two equations (interchangeable), where V = volume, P = pressure, and C = some constant that defines this inverse relationship:

P = 1/V * C = C/V

or

V = 1/P * C = C/P

We have to use the description of the problem to find C:

"The volume of this gas is 175 cm^3 when 3.2 kg/cm^2 of pressure is placed on it"

So lets find C in one of the equations above (remember you can use either one of the 2):

C = P * V

When P = 3.2 kg/cm^2 and V = 175 cm^3 .. C = (3.2kg * 175cm)/cm^3 = 560 cm*kg

I separated out the units so you understand to get the units correctly when doing this on a multiple choice test for example. Sometimes they could trick you with the same numeric answer but different units.

So now lets solve for the pressure when the volume is 400 cm^3 as the problem asks:

P = C/V --> V = 500 cm*kg / 400 cm^3 = 1.4 kg/cm^2

P = 1.4 kg/cm^2

I suggest you review more here to get full clarity on the topic in which this problem has come about, "Inverse and direct variations":

https://www.khanacademy.org/math/algebra-home/alg-rational-expr-eq-func/alg-direct-and-inverse-variation/v/direct-and-inverse-variation

Answer 2

Inverse variation means that the two quantities multiple directly to some common constant.

P1V1=k, P2V2=k, therefore P1V1=P2V2. Substitute with numbers.

3.2 kg/cm^2 * 175cm^3 = P2 * 400cm^3; P2 = 1.4 kg/cm^2