Find the number of pairs of integers (x,y) with 0 < x, y < 10 that satisfy \( \frac{1}{1-\frac{10}{x}} > 1 - \frac{5}{y}.\)
+128407 We can simplify this as
x / [ x - 10 ] > [ y - 5] / y
Since 0 < x, y < 10.....the left side will always be negative
And the right side will be negative when y < 5
So when x = 1
The possible integer values for y are 1, 2, 3 and 4
When x = 2
The possible integer values are 1, 2, 3
When x = 3
The possible integer values of y are 1,2,3
When x = 4
The possible integer values for y are 1, 2
When x = 5
The possible integer values for y are 1,2
When x = 6
The possible values for y are 1
When x = 7
The possible values for y are 1
When x = 8...there is no value of y that makes the inequality true
So....there are 16 pairs of (x, y) that make the inequality true
