Answer :
Sure, let's break down the solution step-by-step.
### Part 1: Finding the Number of Pieces of Rope
1. Length of the Rope: Rahim has a rope that is 30 meters long.
2. Length per Piece: Each piece of the rope is [tex]\(2 \frac{1}{2}\)[/tex] meters long. We can convert this mixed number into an improper fraction:
[tex]\[
2 \frac{1}{2} = 2 + \frac{1}{2} = \frac{4}{2} + \frac{1}{2} = \frac{5}{2}
\][/tex]
So, each piece is [tex]\(2.5\)[/tex] meters long.
3. Calculating the Number of Pieces:
We divide the total length of the rope by the length of each piece:
[tex]\[
\frac{30}{2.5} = 12
\][/tex]
Hence, Rahim gets 12 pieces of the rope.
### Part 2: Finding the Cost of 1 kg of Mangoes
1. Total Cost of Mangoes: The cost of [tex]\(3 \frac{1}{2}\)[/tex] kg of mangoes is [tex]\(₹ 157 \frac{1}{2}\)[/tex]. Converting these into decimal numbers:
- [tex]\(3 \frac{1}{2}\)[/tex] kg = 3.5 kg
- [tex]\(₹ 157 \frac{1}{2}\)[/tex] = ₹ 157.5
2. Cost per kg:
We divide the total cost by the total weight:
[tex]\[
\frac{157.5}{3.5} = 45
\][/tex]
Therefore, the cost of 1 kg of mangoes is ₹ 45.
### Summary of Solutions:
- Rahim cut the 30-meter-long rope into 12 pieces, each 2.5 meters long.
- The cost of 1 kg of mangoes is ₹ 45.
I hope this clear explanation helps you understand how to solve these types of problems! If you have any further questions, feel free to ask.
### Part 1: Finding the Number of Pieces of Rope
1. Length of the Rope: Rahim has a rope that is 30 meters long.
2. Length per Piece: Each piece of the rope is [tex]\(2 \frac{1}{2}\)[/tex] meters long. We can convert this mixed number into an improper fraction:
[tex]\[
2 \frac{1}{2} = 2 + \frac{1}{2} = \frac{4}{2} + \frac{1}{2} = \frac{5}{2}
\][/tex]
So, each piece is [tex]\(2.5\)[/tex] meters long.
3. Calculating the Number of Pieces:
We divide the total length of the rope by the length of each piece:
[tex]\[
\frac{30}{2.5} = 12
\][/tex]
Hence, Rahim gets 12 pieces of the rope.
### Part 2: Finding the Cost of 1 kg of Mangoes
1. Total Cost of Mangoes: The cost of [tex]\(3 \frac{1}{2}\)[/tex] kg of mangoes is [tex]\(₹ 157 \frac{1}{2}\)[/tex]. Converting these into decimal numbers:
- [tex]\(3 \frac{1}{2}\)[/tex] kg = 3.5 kg
- [tex]\(₹ 157 \frac{1}{2}\)[/tex] = ₹ 157.5
2. Cost per kg:
We divide the total cost by the total weight:
[tex]\[
\frac{157.5}{3.5} = 45
\][/tex]
Therefore, the cost of 1 kg of mangoes is ₹ 45.
### Summary of Solutions:
- Rahim cut the 30-meter-long rope into 12 pieces, each 2.5 meters long.
- The cost of 1 kg of mangoes is ₹ 45.
I hope this clear explanation helps you understand how to solve these types of problems! If you have any further questions, feel free to ask.
