Question

Find the greatest possible value for a+b+c+d if b is a positive integer and a,b,c,d satisfy the system of equations

Answer 1

Answer is a+b+c+d= -5.b

Answer 2

Answer:

$a+b+c+d = -5\cdot b$

Step-by-step explanation:

The given system of equations is now reduced:

1) $a+b = c$, $b+c = d$, $c+d=a$, $b > 0$ Given

2) $a = c+d$ By 1)

3) $(c+d)+b=c$ 2) in 1)

4) $d = b + c$ By 1)

5) $[c+(b+c)]+b = c$ 4) in 3)

6) $2\cdot b + 2\cdot c = c$ Algebra

7) $c = -2\cdot b$ Algebra

8) $d = -b$ 7) in 4)/Algebra

9) $a = -3\cdot b$ 7) and 8) in 2)/Algebra

10) $a+b+c+d = -5\cdot b$ 9), 1), 7) and 8)/Algebra/Result