Question 766749
<pre>
if a+b = 65, a+c=63 and a+d=45 what will be the value of "a" if a+b+c+d=118

a + b = 65 (eqn 1)
a + c = 63 (eqn 2)
a + d = 45 (eqn 3)
a + b + c + d = 118 (eqn 4)

Adding eqns (1), (2), and (3), we get
3*a + b + c + d = 65 + 63 + 45 = 173
So, b + c + d = 173 - 3*a   (eqn 5)

Substituting for (b+c+d) in eqn (4)

a + 173 - 3*a = 118
2*a = 173 - 118 = 55
a = {{{highlight(27.5)}}}
Now we can find b, c and d from the first 3 equations
b = 65 - a = 65 - 27.5 = {{{highlight(37.5)}}}
c = 63 - a = 63 - 27.5 = {{{highlight(35.5)}}}
d = 45 - a = 45 - 27.5 = {{{highlight(17.5)}}}

Check for correctness:
a + b + c + d = 27.5 + 37.5 + 35.5 + 17.5 = 118 (correct!)

:)