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?

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

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