**When a number, half of a number, and a third of a number are added together, the sum is 385. Find the three numbers.**

Let's make the mystery number represented as, "n," for 'number.'

We start with n.

We know we're going to be adding things together, so we can add a + sign after our "n."

n+

'Half of a number,' can be expressed by dividing 'n' in half. We can write this out as n/2.

(Confused? Plug in a number! Four, for example, divided by two equals two. Half of four = 2)

'Third of a number," can be expressed by dividing 'n' into thirds. We can write this out as n/3.

When we combine all three of these terms, we come up with:

n + (n/2) + (n/3)

The whole thing equals 385.

n + (n/2) + (n/3) = 385

As suggested in another answer, we can factor out n to deal with our fractions/decimals first. Factoring is simply pulling out pieces (multiples) of a larger number.
**Don't forget that there's an invisible "1" in front of variables (letters representing a mystery number).**

n (1/1 + 1/2 + 1/3) = 385

Now we need to combine terms within the parenthesis. However, we can't add fractions until we've found a common denominator. Six is an easy number to use, since we can multiply (1/2) x 3/3 to get 3/6, and multiply (1/3) x 2/2 to get 2/6. And of course, 1/1 x 6/6 = 6/6.

n (6 + 3 + 2) = 385

6 6 6

n (11) = 385

6

Let's get rid of that ugly fraction. Multiply BOTH sides by 6.

(6) 11n = 385 (6)

6

11n = 2310

To isolate n, we need to divide each side by 11.

11n = 2310

11 11

We end up with:

n = 210

Great, now we know what n is, but what about n/2 and n/3? This is the easy part-
**just plug it in!**

n = 210 = 105

2 2

n = 210 = 70

3 3

Let's check:

n + (n/2) + (n/3) = 385

210 + 105 + 70 = 385

385 = 385