Bob and Wendy live in a house in which the floor of every
room is a square and covered with identical square tiles.
Wendy's room contains 101 tiles more than Bob's room. How
many tiles does Wendy's room contain?
Let x = the number of tiles along one side of Wendy's room.
Then x² = the number of tiles in Wendy's room.
Let y = the number of tiles along one side of Bob's room.
Then y² = the number of tiles in Bob's room.
>>...Wendy's room contains 101 tiles more than Bob's
room...<<
Translation: x² = y² + 101
x² - y² = 101
(x - y)(x + y) = 101
This says (x - y) and (x + y) are both factors of 101
But 101 is a prime number and thus has only two factors,
1 and 101.
Therefore x - y, the smaller one, must equal 1, and
x + y, the larger one, must equal 101. So we solve the
system of equations:
x - y = 1
x + y = 101
and we get x = 51, y = 50
So Wendy's room contains x² or 51² or 2601 tiles
and Bob's room contains y² or 50² or 2500 tiles.
Edwin
