The sum of 2 numbers is 76. 1/3 of the first number plus 1/2 of the second number is 34. What are the two numbers? What is the difference between the second number and first number?

28 difference and the numbers are 13 and 12 121 21 212 12 55 65 545 46 54 6 5 6 6666666 777.0-0000000

Ok so we have 2 equations here ...

x + y = 76

1/3x + 1/2y = 34

First solve for x in the 1st equation ...

x + y = 76

x = 76 - y

Now substitute 76-y for x in the 2nd equation ...

1/3x + 1/2y = 34

1/3 (76-y) + 1/2y = 34

76/3 - 1/3y + 1/2y = 34

-1/3y + 1/2y = 34 - 76/3

-2/6y + 3/6y = 34 - 25 1/3

1/6y = 8 2/3

y = 8 2/3 : 1/6

y = 8 2/3 * 6

y = 52

Now substitute 52 into the 1st equation for y

x + y = 76

x + 52 = 76

x = 76 - 52

x = 24

The 2 numbers are 24 and 52.

The difference between the numbers is

52 - 24 = 28