a).
The 8" by 7" tile covers 49 square inches.
The 21" by 21" tile covers 441 square inches.
b).
The area of the floor is (420" x 630") = 264,600 square inches.
c).
It would take (264,600) / (441) = 600 large tiles to cover the floor.
d).
Emmanuel should use the big tiles to cover his floor.
-- A big tile costs 4 times as much as a small tile, but it has 9 times
as much area as a little tile has, so it is a better buy.
-- Plus, he would have to pay the floorman a lot more to glue down 5,400 tiles
than he will have to pay to glue down only 600 tiles.
-- Since he has hired my services to advise him, I will charge him only 15%
of the difference if he takes my advice, so he will still be money ahead.