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

**Don't forget that there's an invisible "1" in front of variables (letters representing a mystery number).**

**just plug it in!**

3 3

Addie K.

asked • 12/05/13This word problem has me stumped.. I would really lovesome step by step help, thanks!

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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

3 3

Let's check:

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

210 + 105 + 70 = 385

385 = 385

Benjamin M. answered • 12/05/13

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CSUN Grad, tutoring Mathematics Science

This is a question about variables. It's asking you to substitute a variable for the "number" referred to in the problem.

Basically, you have to know how to put that "number" in an equation.

"a number" means x

"half of a number" means x times one half = x/2

"a third of a number" means x times one third = x/3

Once you know that, the equation sorts itself out

a number, half of a number, and a third of a number are added together, the sum is 385

means

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

After lots of un-fun algebra you can solve for x

x + x/2 + x/3 = 385

x(1+1/2+1/3) = 385 <----factoring out x

now, 1 + 1/2 + 1/3 looks ugly, but its easier if we look at it this way

1/1 + 1/2 + 1/3

now it's a fraction addition problem

the common denominator of 1, 2, and 3 is 6, so

1/1 + 1/2 + 1/3 =

6/6 + 3/6 + 2/6 = 11/6

so 1 + 1/2 + 1/3 = 11/6 (let's leave it as an improper fraction for now.)

back to the problem:

x(11/6) = 385 <---to "cancel" 11/6, we multiply by 6, then divide by 11

6*x*(11/6) = 385*6

11x = 2310

11x/11 = 2310/11

x = 210

Great! But the question didnt' ask for x, it asked for the three numbers.

So, back to our original equation.

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

If x = 210, then

x/2 means 210/2, or 105

and

x/3 means 210/3, or 70

So the "number" is 210, the "half of a number" is 105, and the "a third of a number" is 70.

Steve P. answered • 12/05/13

Tutor

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Patient and Knowledgable Math and Chemistry Tutor

x+1/2x+1/3x=385

FInd the common denominator so you can add the fractions:

6/6x+3/6x+2/6x=385

Multiply both sides by 6/11

6/11(11/6x)= 6/11(385)

x=210

1/2(210)=105

1/3(210)=70

The 3 numbers are 70,105 and 210

70+105+210=385

Steve S. answered • 12/05/13

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5
(3)
Tutoring in Precalculus, Trig, and Differential Calculus

When a number (x), half of a number (x/2), and a third of a number (x/3) are added together (x+x/2+x/3), the sum is 385 (x+x/2+x/3=385).

Let's multiply both sides of the equation by 2*3=6:

6x+2*3*(x/2)+2*3*(x/3)=6*385

Simplify; expressing 385 as a product of prime factors:

6x+3x+2x=6*5*7*11

11x=210*11

x=210

x/2 = 105

x/3 = 70

check: 210+105+70=385 √

Vivian L. answered • 12/05/13

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Microsoft Word/Excel/Outlook, essay composition, math; I LOVE TO TEACH

Hi Addie;

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

Let's multiply both sides by 6 (2 x 3) to eliminate the fractions...

6[x+(x/2)+(x/3)]=(385)(6)

6x+3x+2x=2310

11x=2310

Let's divide both sides by 11...

(11x)/11=2310/11

x=210

x/2=105

x/3=70

Let's check our work...

210+105+70=385

385=385

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