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