The sum of two numbers is 3 3/4 if 1/3 of the larger number is 1/2 more than 2/3 of the smaller find the number

Let us assume the larger number = x

Let us assume the smaller number = y

Then

x + y = 3 3/4

x + y = 15/4

And

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

x = [3 * (2y/3) ] + (3/2)

= 2y + (3/2)

Now putting the value of x from the second equation to the first, we get

x + y = 15/4

2y + (3/2) + y = 15/4

3y = (15/4) - (3/2)

3y = (15 - 6) / 4

3y * 4 = 9

12y = 9

y = 9/12

= 3/4

Now putting the value of y in the first equation, we get

x + y = 15/4

x + (3/4) = (15/4)

x = (15/4) - (3/4)

= (15 - 3) / 4

= 12/4

= 3

So the value of x or the larger number is 3 and the value of y or the smaller number is 3/4.