The larger of two number is 12 more than smaller number. if the sum of the two numbers is 74,find the two numbers

The first number is 12 more than the second number.

This means that if you subtract 12 from the first number, you'll get the second number.  Let's have x stand for the first, larger number, and y stand for the second, smaller number.

74 = x + y

x = y + 12

So 74 = y + y + 12 which simplifies to 74 = 2y + 12.

Now all we need to do is solve the equation to find y.  First, we'll subtract both sides by 12:

74 - 12 = 62.

2y + 12 - 12 = 2y.

Now we have 62 = 2y.  Dividing both sides by 2 gives us:

31 = y.  (y is the second, smaller number)

Now we need to find x.  Recall our previous equation which tells us that x = y + 12.

Plug in y = 31 to get:

x = 31 + 12

x = 43

Let's check to make sure this is right.  43 + 31 give us 74.  43 is 12 more than 31.  So, our two numbers are 43 and 31.