What is the difference between the second number and the first number?

 The sum of two numbers is 76. One-third of the first number plus half of the second number is 34. What is the difference between the second number and the first number?

Let us define the first number as x and the second number as y. We can write the following two equations

x + y = 76 .......... (a). This equation is derived from the statement "the sum of the 2 numbers is 76"

1/3 x + 1/2 y = 34 ............ (b). This equation is derived from the statement " 1/3 of the first number plus 1/2 the second number is 34. 

Now let's multiply (b) by 6

2x + 3y = 204 ............ (c)

Now multiply (a) by 2

2x + 2y = 152 ............ (d)

Subtract d from c to find out what the second number (y) is. 

y = 204 - 152 = 52

Now plug y into equation (a) to solve for the first number (x). 

x + 52 = 76

Subtracting 52 from both sides we get:

x = 76-52 = 24

Now we know that the first number is 24 and the second number is 52, but we are asked for the difference between the two numbers. 

52 - 24 = 28

Ans: 28