Question

If
a+b = 8
a*c = 21
c*d = 9
and b-d=5

Find the values of a,b,c and d

Answer 1

The values are A = 2.1  , B = 5.9  , C = 10 and D = 0.9

Step-by-step explanation:

Using simple method:

• A  + B  = 8
• A = 8 - B

(8 - B ) x C = 21

8 C - B C = 21  ------ (1)

D = B- 5

C x ( B  - 5 ) = 9

B C - 5 C = 9   ------- (2)

Adding equations (1) and (2)

3 C = 30

C = 10

A = 2.1

B = 5.9

C = 10

D = 0.9

Answer 2

Given:

a+b = 8

a*c = 21

c*d = 9

b-d=5

To find:

a, b, c, d =?

Solution:

$a+b = 8.....(i)\\a*c = 21.....(ii)\\c*d = 9.....(iii)\\b-d=5......(iv)$

let, divide the equation (ii) from equation (i) and put the value in equation (i):

$\Rightarrow \frac{ac}{cd}= \frac{21}{9}\\\\\Rightarrow \frac{a}{d}= \frac{7}{3}\\\\\Rightarrow a= \frac{7d}{3}$

Equation:

$\Rightarrow a+b=8\\\\\Rightarrow \frac{7d}{3}+b=8\\\\\Rightarrow \frac{7d+3b}{3}=8\\\\\Rightarrow 7d+3b=24.....(a)$

Solve the equation (iv) and put the value into the equation (a):

$\Rightarrow b-d=5\\\\\Rightarrow b=5+d\\\\\ equation: \\\\ \bold{\Rightarrow 7d+3b=24}\\\\\Rightarrow 7d+3(5+d)=24\\\\\Rightarrow 7d+15+3d=24\\\\\Rightarrow 10d+15=24\\\\\Rightarrow 10d=24-15\\\\\Rightarrow 10d=9\\\\\Rightarrow d= \frac{9}{10}\\\\\Rightarrow d= 0.9$

put the value of d in the equation (iv):

$\Rightarrow b-0.9=5\\\\\Rightarrow b=5+0.9\\\\\Rightarrow b=5.9$

put the value b into the equation (i):

$\Rightarrow a+5.9=8\\\\\Rightarrow a=8-5.9\\\\\Rightarrow a=2.1$

put the value of a in to the equation (ii):

$\Rightarrow 2.1*c=21\\\\\Rightarrow c=\frac{21}{2.1}\\\\\Rightarrow c=\frac{210}{21}\\\\\Rightarrow c=10$

The final value of a, b, c, d is: 2.1, 5.9, 10, 0.9