Question

You want to put a 5 inch thick layer of topsoil for a new 23 ft by 18 ft garden. the dirt store sells by the cubic yards. how many cubic yards will you need to order? the store only sells in increments of 1/4 cubic yards.

Answer 1

You need to buy 6.5 cubic yards.

Explanation:

You want to put a 5 inch thick layer of topsoil for a new 23 ft by 18 ft garden.

We know 1 yard = 3 feet or 1 yard = 36 inches

Then 1 inch =
`1/36` yard.

1 feet = 1/3 yard

The volume of the layer of the topsoil is given by:

=
`5(1/36)(23)(1/3)(18)(1/3)` cubic yards

`2070/324=6.39` cubic yards

Now, the store only sells increments of 1/4 = 0.25 cubic yards.

So, we need to buy
`6.39/0.25=25.56` increments

Rounded to 26 increments.

Therefore, we need to buy 26 increments of 1/4 cubic yards.

That becomes 6.5 cubic yards.

Answer 2

5 inches = 5/12 = 0.4166 feet

23 x 18 x 0.4166 = 172.5 cubic feet

1 cubic foot = 0.037037 cubic yards

172.5 x 0.037037 = 6.39 round up to 6.5 cubic yards