Determine the volume of atmospheric air (at 14 lb/in.^2) needed to fill your bike tires (assuming it holds 500 ml of air) to the pressure recommended by the manufacturer (70 lb/in.^2)

Boyle Law says “the pressure of fixed amount of ideal gas which is at constant temperature is inversely proportional to its volume".

P = 1/V

Where, P is pressure of the ideal gas and V is volume of the ideal gas.

For two situations, this law can be added as;
P₁V₁ = P₂V₂

14 lb/in² x V₁ = 70 lb/in² x 500 mL
                 V₁ = 2500 mL

Hence, the needed volume of atmospheric air = 2500 mL

Here, we made two assumptions. They are,
1. The atmospheric air acts as ideal gas.
2. Temperature is a constant.

We didn't convert the units to SI units since converting volume and pressure are products of two numbers, they will cut off. 

the answer is 303.15 or 303