Question

the number of integral points (x,y) which lie in first quadrant but not on coordinate axes and also on straight line 3x+5y = 2007 is ?

Answer 1

Answer:

133

Step-by-step explanation:

We need 2007 - 3x to be a multiple of 5.  Dividing by 3, this means we need 669 - x to be a multiple of 5.  This means we need x itself to be one less than a multiple of 5.

Also, we need 2007 - 3x to be positive (not zero!), so we need

x ≤ 668.

Putting the two facts together, x must be one of the following values:

4, 9, 14, 19, 24, 29, ..., 659, 664.

The answer is just how many values there are in this list.  This is an arithmetic progression with common difference 5, so the number of terms is

1 + ( 664 - 4 ) / 5 = 133

Answer 2

Answer:

133

Step-by-step explanation:

We need 2007 - 3x to be a multiple of 5.  Dividing by 3, this means we need 669 - x to be a multiple of 5.  This means we need x itself to be one less than a multiple of 5.

Also, we need 2007 - 3x to be positive (not zero!), so we need

x ≤ 668.

Putting the two facts together, x must be one of the following values:

4, 9, 14, 19, 24, 29, ..., 659, 664.

The answer is just how many values there are in this list.  This is an arithmetic progression with common difference 5, so the number of terms is

1 + ( 664 - 4 ) / 5 = 133