Answer:
The least is 5
Step-by-step explanation:
Represent the numbers with x, y and z.
Such that:
[tex]x + y = 12[/tex]
[tex]y + z = 17[/tex]
[tex]x + z = 19[/tex]
Required
Determine the smallest number
Add the three equations:
[tex](x + y) + (y + z) + (x + z) = 12 + 17 + 19[/tex]
[tex](x + y) + (y + z) + (x + z) = 48[/tex]
Collect Like Terms
[tex]x + x + y + y + z + z = 48[/tex]
[tex]2x + 2y + 2z= 48[/tex]
Divide through by 2
[tex]x + y +z = 24[/tex]
Recall that:
[tex]x + y = 12[/tex]
[tex]y + z = 17[/tex]
[tex]x + z = 19[/tex]
Substitute 12 for x + y in [tex]x + y +z = 24[/tex]
[tex]12 + z =24[/tex]
[tex]z = 24-12[/tex]
[tex]z = 12[/tex]
Substitute 17 for y + z in [tex]x + y +z = 24[/tex]
[tex]x + 17 = 24[/tex]
[tex]x = 24-17[/tex]
[tex]x = 7[/tex]
Substitute 19 for x + z in [tex]x + y +z = 24[/tex]
[tex]19 + y = 24[/tex]
[tex]y = 24 - 19[/tex]
[tex]y = 5[/tex]
So:
The numbers are 7, 5 and 12 and the least is 5
