Question 1203135
the set of whole numbers is all positive integers plus 0.
you are given that x + y = 45 and x - y < 10
from the first equation, solve for y to get y = 45 - x
in the second equation, replace y with 45 - x to get x - (45 - x) < 10 which becomes 2x - 45 < 10 which becomes 2x < 55 which becomes x < 27.5.
since x has to be a whole number, you get x <= 27.
when x = 27, y = 45 - 27 = 18 and x - y becomes 27 - 18 = 9
when x = 26, y = 45 - 26 = 19 and x - y becomes 27 - 19 = 7
working down the line, you get:
when x = 25, x - y = 5
when x = 24, x - y = 3
when x = 23, x - y = 1
when x = 22, x - y = -1 ***** this is not a whole number.
you run out of x - y being a whole number after x = 23, so you have to stop there.
your total of possible values of x - y < 10 is equal to 5.
that's your solution.