need help with a few quests. Thanks so much

Question

You want to put a 2 inch thick layer of topsoil for a new 27 ft by 32 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

2/12 x 27 x 32

= 1/6 x 27 x 32

= 9 x 16 = 144 ft^3

1 cubic yard = 3^3 = 127 ft^3

divide 144 x 1/9 = 144/27 = 16/3 = 5 1/3

sold in increments of 1/4 means

4 x 16/3 = 64/3 = 21 and 1/3 purchases

or 22 needed

Answer 2

2 inches = 1/6 of a foot

Volume of topsoil needed = (1/6 ft)(27 ft)(32 ft) = 144 ft³ (1 yd / 3 ft)³ = 5 1/3 yd³

1/4 = 3/12 and 1/3 = 4/12

Buy 5 1/2 yd³ (5 1/4 is short by 1/12 yd³)