Question

the difference between two numbers is 8 if 2 is added to the bigger number the result will be 3 times the smaller number find the numbers

Answer 1

Hey mate..
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Let the smaller number be x

And the bigger number be y

Given,

The difference between two numbers is 8

So,

y - x = 8....(1)

Also,

If 2 is added to the bigger number the result will be 3 times the smaller number.

So,

=> 2 + y = 3x

=> 3x - y = 2......(2)

Adding Eq. (2) From Eq.(1) we get,

=> ( y - x ) + ( 3x - y ) = 8 - 2

=> y - x + 3x - y = 6

=> 2x = 6

=> x = 6 / 2

=> x = 3

Putting the value of x = 3 in Eq. (1) we get ,

=> y - 3 = 2

=> y = 2 + 3

=> y = 5

Thus,

The required values of x and y are 3 and 5 respectively.

Hope it helps !!

Answer 2

Let the numbers be a and b

a-b = 8               ..........(a)

(a+2) - b = 3b
a+2 = 4b
a = 4b-2        ................(b)

Substituting in (a),
4b-2-b = 8
3b = 10
b = 3.5
a - b = 8
a = 11.5