Question

When the greater of the two numbers increased by 1 divides the sum of the numbers the result is3/2 .when the difference of these numbers is divide by the smaller ,the result is 1/2 .find the numbers

Answer 1

If x < y, then we have

(x+y)/(y+1) = 3/2
(y-x)/x = 1/2

Now just solve for x and y

Answer 2

a = the greater number

b = the smaller number


When the greater of the two numbers increased by 1 divides the sum of the numbers the result is 3 / 2 mean :

( a + 1 ) / ( a + b ) = 3 / 2

When the difference of these numbers is divide by the smaller ,the result is 1 / 2 mean:

( a - b ) / b = 1 / 2

Now you must solve system:

( a + 1 ) / ( a + b ) = 3 / 2

( a - b ) / b = 1 / 2


( a - b ) / b = 1 / 2 Multiply both sides by b

a - b = b / 2 Add b to both sides

a - b + b = b / 2 + b

a = b / 2 + b

a = b / 2 + 2 b / 2

a = 3 b / 2


Replace this value in equation:

( a + 1 ) / ( a + b ) = 3 / 2

( 3 b / 2 + 1 ) / ( 3 b / 2 + b ) = 3 / 2

( 3 b / 2 + 2 / 2 ) / ( 3 b / 2 + 2 b / 2 ) = 3 / 2

[ ( 3 b + 2 ) / 2 ] / ( 5 b / 2 ) = 3 / 2

2 * ( 3 b + 2 ) / ( 2 * 5 b ) = 3 / 2

( 3 b + 2 ) / 5 b = 3 / 2 Multiply both sides by 5 b

3 b + 2 = 3 * 5 b / 2

3 b + 2 = 15 b / 2 Multiply both sides by 2

2 * ( 3 b + 2 ) = 15 b

6 b + 4 = 15 b Subtract 6 b to both sides

6 b + 4 - 6 b = 15 b - 6 b

4 = 9 b Divide both sides by 9

4 / 9 = b

b = 4 / 9


Replace this value in equation:

a = 3 b / 2

a = ( 3 * 4 / 9 ) / 2

a = 12 / ( 2 * 9 )

a = 12 / 18

a = 6 * 2 / 6 * 3

a = 2 / 3


The solutions are:

a = 2 / 3 , b = 4 / 9


Proof:

( a + 1 ) / ( a + b ) = 3 / 2

( 2 / 3 + 1 ) / ( 2 / 3 + 4 / 9 ) =

( 2 / 3 + 3 / 3 ) / ( 3 * 2 / 3 * 3 + 4 / 9 ) =

( 5 / 3 ) / ( 6 / 9 + 4 / 9 ) =

( 5 / 3 ) / (10 / 9 ) =

5 * 9 / 3 * 10 =

5 * 3 * 3 / 3 * 5 * 2 =

3 / 2


( a - b ) / b = 1 / 2

( 2 / 3 - 4 / 9 ) / ( 4 / 9 ) =

( 2 * 3 / 3 * 3 - 4 / 9 ) / ( 4 / 9 ) =

( 6 / 9 - 4 / 9 ) / ( 4 / 9 ) =

( 2 / 9 ) / ( 4 / 9 ) =

2 * 9 / 4 * 9 =

2 / 4 = 1 * 2 / 2 * 2 = 1 / 2

Answer 3

Hmm. I got 6 and 9

Better read the problem again. You got your division backwards: the greater divides the sum.