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## Homework Statement

I'm trying to understand algebraically how the solution was arrived at for the following problem.

Automobile tire at normal atmosphere at 10 deg C.

Inflating the tire to 28% of original volume with an increase in temp to 40 deg C

What is the pressure?

## Homework Equations

PV = nRT where P is the pressure, V is the volume, n is the number of moles, R is a constant, and T is the temp

## The Attempt at a Solution

The the solution is given in what appears as a ratio between the initial values and final values, and I'm just not understanding algebraically how the equation in step 1. was derived. Why would I divide the final values with the initial values?

1. (P_2)(V_2) / (P_1)(V_1) = nRT_2 / nRT_1

2. (P_2)(.28V_1) / (1 atm)(V_1) = T_2 / T_1

3. (.28)P_2) / (1 atm) = 313.15 K / 283.15 K

4. P_2 = 1.106 / .28

5. P_2 = 3.95 atm

Thanks for whatever enlightenment you might be able to give.