One number is 6 more than a second number, the sum of the two numbers is 330. what are the numbers?show work you

Let's have the first number, the larger number, be x.  We'll have the second, smaller number be y.

We know that x = y + 6, since x is 6 greater than y.

We also know that 330 = x + y.

Because x = y + 6, 330 = y + 6 + y, which simplifies to 330 = 2y + 6.

Now all we need to do is simplify the equation.  First, we subtract 6 from both sides:

330 - 6 = 324

2y + 6 - 6 = 2y.

So we have 324 = 2y.  Then we divide both sides by 2 to get:

162 = y

Plug in y = 162 into the equation x = y + 6 to get:

x = 162 + 6

x = 168

Let's check to make sure our answer is right.  168 is 6 more than 162.  162 + 168 equals 330.  So our two numbers are 168 and 162.

x = 12

y = 15

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