Question

A+b=21 b+c=24 c+d=32 d+e=37 e+f=31 f+g=25 g+a=26 find a,b,c,d,e,f,g,

Answer 1

Answer:

a = 12

b = 9

c = 15

d = 17

e = 20

f = 11

g = 14

Step-by-step explanation:

Given that

(a + b) = 21 ...... (1)

(b + c) = 24 ........ (2)

(c + d) = 32 ........ (3)

(d + e) = 37 ........ (4)

(e + f) = 31 .......... (5)

(f + g) = 25 ........ (6)

(g + a) = 26 ......... (7)

Hence, adding all the equations we get, 2(a + b + c + d + e + f + g) = 196

⇒ (a + b + c + d + e + f + g) = 98 ...... (8)

Adding equations (2), (4) and (6), we get (b + c + d + e + f + g) = 86.

Therefore, from equation (8), we get a = 98 - 86 = 12 (Answer)

Adding equations (3), (5), and (7) we get,

a + c + d + e + f + g = 89

Hence, from equation (8), we have b = 98 - 89 = 9 (Answer)

Similarly, adding equations (1), (4), and (6) we get,

a + b + d + e + f + g = 83,

Hence, c = 98 - 83 = 15 (Answer)

Now, adding equations (2), (5) and (7), we get

a + b + c + e + f + g = 81. Hence, d = 98 -81 = 17 (Answer)

Adding equations (1), (3), and (6)

a + b + c + d + f + g = 78. Hence e = 98 - 78 = 20 (Answer)

Adding equations (2), (4), and (7)

a + b + c + d + e + g = 87. Hence f = 98 - 87 = 11 (Answer)

Adding equations (1), (3), and (5)

a + b + c + d + e + f = 84. Hence g = 98 - 84 = 14 (Answer)