a piece of string is cut in half, so that one half can be used to tie newspapers, one third of the remaining string is cut off to tie a parcel. the leftover string is 2m long. how long was the whole string

String is x meters long.

The string is cut in 1/2 so now we have 2 halves, each half is (1/2)*x or x/2.
We take 1/3 of the x/2 piece to tie a parcel. How much is left? That will be
(1/2)(x)-(1/3)(x/2) and that piece is 2 m.

So (1/2)(x)-(1/3)(x/2) = 2 m
or (1/2)(x)-(1/6)(x) = 6
Solve for x.
Multiply through by 6.
3x-x=12
2x = 12
x = 6,
Check:
String is 6 meters long.
We cut half of it leaving 3 meters.
3 meters used to tie newspaper.
The 3 meter piece that's left is cut to remove 1/3 of that. 1/3*3 = 1 meter used to tie a parcel. That leaves 2 meters for the part left over and that's what the problem says.

6m

6m

Oh, the poor string must be feeling quite sliced and diced! Let me do some math to untangle this conundrum for you.

If one half of the string is used to tie newspapers, that means the remaining half is left, which we'll call x meters.

Next, one third of this remaining string is cut off to tie a parcel. That means we're left with two-thirds of x meters, or (2/3)x meters.

According to the information provided, this leftover string measures 2 meters. So we can set up an equation:

(2/3)x = 2

To find x, we multiply both sides of the equation by 3/2:

x = (2 * 3) / 2

Simplifying that, x = 3 meters.

Now, we know that one half of the string is x meters, so the whole string must be double that: 2 * 3 = 6 meters.

Thus, the whole string was 6 meters long, which is quite the length for tying newspapers and parcels! Keep that string in check, my friend!

To find the length of the whole string, let's work step by step.

Step 1:
We know that half of the string was used to tie the newspapers. So, after this step, we are left with half of the original string.
Let's call the original length of the string "x". After tying the newspapers, we have x/2 length of string remaining.

Step 2:
Now, one-third of the remaining string is cut off to tie a parcel. This means we are left with two-thirds of x/2 length of the string.
Mathematically, it can be represented as (2/3) * (x/2).

Step 3:
According to the problem, we are left with 2 meters of string after the above two steps.
So, (2/3) * (x/2) should be equal to 2.

Let's solve the equation to find the value of x:

(2/3) * (x/2) = 2

Cross-multiplying gives us:

2 * 2 = 3 * (x/2)

4 = 3 * (x/2)

Now, multiply both sides by 2/3 to isolate x:

(4 * 2/3) = x

2.67 = x

Therefore, the original length of the string was approximately 2.67 meters (or 267 centimeters).

tbh guys idk

hope this helps you