Tricky Word Problem

Question

This word problem has me stumped..  I would really lovesome step by step help, thanks!

 

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

Answer 1

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

Answer 2

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.

Answer 3

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

 

Answer 4

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 √

Answer 5

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