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
