Question 1150362
Lets first make sure all units are consistent. For the purposes of this problem, let's work with Feet.

Thickness = 5 inches = 5/12ft
Area = 22ftx27ft = {{{ 594 ft^2}}}
Therefore volume of dirt needed to fill the yard is  Area x Thickness = {{{247.5ft^3}}}

We can calculate the volume of dirt in each "order" by converting to ft
1/4 cubic yards = (1 yard = 3 feet) >> {{{ ((3)^3)/4}}} = {{{ 6.75ft^3}}}

To find how many bags of orders we need we divide (total volume needed) by (volume of dirt in each order)

Solving gives {{{247.5/6.75 = 36.67}}} So we will round to the next whole number and will need 37 orders of dirt.