Question

Half the difference between two numbers is 2. The sum of the greater number and twice the smaller number is 13. Find the numbers.

Answer 1

Answer:

The numbers are

7 and 3

Solution :

Let greater number be x and smaller number be y

1/2( x-y)=2

Then x-y=4

According to second situation ,

x+2y=13

on subtracting eq 2 from eq 3

x+2y-(x-y) =13-4

x+2y-x+y=9

3y=9

y=3

on putting value of y on eq 2

x-y=4

x=4+y=4+3=7

Greater number is 7

and

Smaller number is 3

Answer 2

The greater number is 7.

The smaller number is 3.

Given: The sum of the greater number and twice the smaller number is 13 and a half the difference between two numbers is 2.  

To Find: The value of the numbers.

Solution:

Let the greater numbers be 'x' and the smaller number 'y'.

It is said that half the difference between the two numbers is 2. So, we can write it as;

    1 / 2 × ( x - y ) = 2

⇒  ( x - y ) = 4                                                                         ....(1)

It is also said that the sum of the greater number and twice the smaller number is 13. So, we can write it as;

     x + 2y = 13                                                                        ....(2)

Subtracting (2) from (1), we get;

     ( x - y ) - ( x + 2y ) = 4 - 13

⇒  x - y - x - 2y = - 9

⇒  - 3y = - 9

⇒   y = 9 / 3

⇒   y = 3

Putting y = 3 in (1), we get;

      x - y  = 4    

 ⇒  x - 3 = 4

 ⇒  x = 4 + 3

 ⇒  x = 7

Hence, the greater number is 7.

The smaller number is 3.

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