Answer:
[tex]Sum = 64[/tex]
Step-by-step explanation:
Let the three numbers be a, b and c; such that:
[tex]a + b = 29[/tex] ---- (1)
[tex]b + c = 46[/tex] --- (2)
[tex]a + c = 53[/tex] --- (3)
Subtract equation 2 from 3
[tex]a - b + c - c = 53 - 46[/tex]
[tex]a - b = 7[/tex] --- (4)
Add this equation to the (1)
[tex]a + a + b - b = 29 + 7[/tex]
[tex]2a= 36[/tex]
Solve for a
[tex]a = 36/2[/tex]
[tex]a = 18[/tex]
Substitute 18 for a in (1)
[tex]a + b = 29[/tex]
[tex]18 + b = 29[/tex]
Solve for b
[tex]b = 29 - 18[/tex]
[tex]b = 11[/tex]
Substitute 11 for b in (2)
[tex]b + c = 46[/tex]
[tex]11 + c = 46[/tex]
Solve for c
[tex]c = 46 - 11[/tex]
[tex]c = 35[/tex]
[tex]Sum = a + b +c[/tex]
[tex]Sum = 18 + 11 + 35[/tex]
[tex]Sum = 64[/tex]
