Question

If "(a+b):(b+c):(c+a)=5:7:6" and "2a-3b+4c=66" then value of "c" will be?​

Answer 1

Answer:

c=4

Step-by-step explanation:

a +b=5

a= 5-b

b+c=7

b=7-c

substitute finally

c=4

Answer 2

The value of c would be 24

Step-by-step explanation:

Given,

(a+b):(b+c):(c+a)=5:7:6            ........(1),

2a-3b+4c=66                         .........(2),

From (1),

$\frac{a+b}{b+c}=\frac{5}{7}$

$7a+7b=5b+5c$

$7a+7b-5b-5c=0$

$7a+2b-5c=0$                  .........(3),

Again from equation (1),

$\frac{b+c}{c+a}=\frac{7}{6}$

$6b+6c=7c+7a$

$6b+6c-7c-7a=0$

$-7a+6b-c=0$                  .............(4)

Equation (3) + equation (4),

$8b-6c=0$                      .............(5),

2 × Equation (4) + 7 × Equation (2),

-14a + 12b - 2c + 14a - 21b + 28c = 462

-9b + 26c = 462           ..........(6)

9 × equation (5) + 8 × equation (6),

-54c + 208c = 462

154c = 3696

$\implies c =\frac{3696}{154}=24$

Hence, the value of c is 24.

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