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A rope is cut into equal pieces, and 4 of the pieces are used to tie up packages. The fraction below shows how much of the rope is left over. According to the fraction, into how many pieces was the rope cut?

[tex]\[ \frac{6}{10} \][/tex]

A. 10
B. 2
C. 6
D. 4


Sagot :

To determine into how many pieces the rope was originally cut, let's follow these steps:

1. Understand the problem:
- You have a rope that is cut into equal pieces.
- 4 of these pieces are used to tie up packages.
- The fraction of the rope that is left over is [tex]\(\frac{6}{10}\)[/tex].

2. Define the unknown:
- Let [tex]\( n \)[/tex] be the total number of pieces the rope was cut into.

3. Set up an equation:
- If we start with [tex]\( n \)[/tex] total pieces and use 4 pieces, the number of pieces left over is [tex]\( n - 4 \)[/tex].
- The fraction of the rope left over is given as [tex]\(\frac{6}{10}\)[/tex]. This can be written as:
[tex]\[ \frac{n - 4}{n} = \frac{6}{10} \][/tex]

4. Solve the equation:
- We need to solve for [tex]\( n \)[/tex] in the fraction [tex]\(\frac{n - 4}{n} = \frac{6}{10}\)[/tex].
- By cross-multiplying, we get:
[tex]\[ 10(n - 4) = 6n \][/tex]
- Distribute the 10:
[tex]\[ 10n - 40 = 6n \][/tex]
- Move all terms involving [tex]\( n \)[/tex] to one side:
[tex]\[ 10n - 6n = 40 \][/tex]
- Simplify:
[tex]\[ 4n = 40 \][/tex]
- Divide both sides by 4:
[tex]\[ n = 10 \][/tex]

So, the rope was originally cut into a total of 10 pieces.

Answer: A. 10