Problema Solution
find three odd integers such that their sum is five more than four times the largest integer
Answer provided by our tutors
Let x, y and z represent the three odd integers and x <= y <= z, that is z is the largest.
x + y + z = 5 + 4z
x + y = 5 + 4z - z
x + y = 5 + 3z
Since z > y and z > x we have
5 + 3z > 5 + x + y + z
that is
x + y > 5 + x + y + z
-5 > z
For example for z = -9 we have
x + y = 5 + 3*(-9)
x + y = -22
x = -11
y = -11
Indeed
-11 - 11 - 9 = - 31
5+4*(-9) = 5 - 36 = -31
Such three odd numbers are -11, -11 and -9.