Question

The sum of the present ages of A and B is 40 years. After 4 years, the age of A will be 3 times that of B. What is the present age of B?​

Answer 1

Find the present age of B

Definition:

A mathematical statement in which two expressions on both the left hand side and the right hand side of an equality symbol are equal is an equation.

Step-by-step explanation:

Let x be the present age of A,and y be the present age of B,so

$x+y=40$       (1)

After 4 years,the age of A will be 3 times that of B,so it is expressed as follows,

[tex]x+4=3(y+4)\\ x+4=3y+12\\ x-3y=12-4\\ x-3y=8[/tex]    (2)

Subtract equation (1) and (2)

$x+y=40$

$x-3y=8$

(-)   (+)    (-)

________

[tex]4y=32\\ y=8[/tex]

Substitute $y=8$ in equation (1)

[tex]x+y=40\\ x+8=40\\ x=40-8\\ x=32[/tex]

Therefore,the present age of A is 32 and B is 8.

Answer 2

Given:

Sum of ages of A and B = 40

After 4 years age of A = 3 of B.

To Find:

The present age of B

Solution:

Let the present age of A = x

Let the present age if B = y

Thus,  

x + y = 40

according to question -

x + 4 = 3(y+4)

x + 4 = 3y + 12

x - 3y = 8

Now, substravting equation 1 and 2 -

x + y = 40

x - 3y = 8

= 4y = 32

y = 32/4

y = 8

Answer: Present age of B is 8.