Welcome to Westonci.ca, where your questions are met with accurate answers from a community of experts and enthusiasts. Our Q&A platform offers a seamless experience for finding reliable answers from experts in various disciplines. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.
Sagot :
Let's tackle these two problems step by step.
### Problem 1: Finding the cost of [tex]\(3 \frac{3}{4} \, \text{kg}\)[/tex] of tomatoes
1. Understand the given values:
- The cost of [tex]\(8 \frac{1}{4} \; \text{kg}\)[/tex] of tomatoes is [tex]\(₹ 194 \frac{1}{4}\)[/tex].
2. Convert mixed numbers to improper fractions for easier calculations:
- [tex]\(8 \frac{1}{4} = 8 + \frac{1}{4} = \frac{32}{4} + \frac{1}{4} = \frac{33}{4} \, \text{kg}\)[/tex]
- [tex]\(194 \frac{1}{4} = 194 + \frac{1}{4} = \frac{776}{4} + \frac{1}{4} = \frac{777}{4} \, ₹\)[/tex]
3. Find the cost per kilogram:
- Cost per kg = Total cost / Total weight
- Cost per kg = [tex]\( \frac{\frac{777}{4}}{\frac{33}{4}} = \frac{777}{33} = 23.5454545454545 \, ₹/ \; \text{kg} \)[/tex]
4. Calculate the cost for [tex]\(3 \frac{3}{4} \, \text{kg}\)[/tex]:
- Convert [tex]\(3 \frac{3}{4}\)[/tex] to an improper fraction:
[tex]\(3 \frac{3}{4} = 3 + \frac{3}{4} = \frac{12}{4} + \frac{3}{4} = \frac{15}{4} \, \text{kg}\)[/tex]
- Total cost = Cost per kg [tex]\(*\)[/tex] weight in kg
- Total cost = [tex]\( 23.5454545454545 \times \frac{15}{4} = 88.2954545454545 \, ₹ \)[/tex]
### Problem 2: Finding how many jars each of capacity [tex]\(2 \frac{1}{4} \, \text{l}\)[/tex] can be filled from a tank of [tex]\(28 \frac{1}{8} \, \text{l}\)[/tex]
1. Understand the given values:
- Tank capacity: [tex]\(28 \frac{1}{8} \, \text{l}\)[/tex]
- Jar capacity: [tex]\(2 \frac{1}{4} \, \text{l}\)[/tex]
2. Convert mixed numbers to improper fractions for easier calculations:
- Tank capacity: [tex]\(28 \frac{1}{8} = 28 + \frac{1}{8} = \frac{224}{8} + \frac{1}{8} = \frac{225}{8} \, \text{l}\)[/tex]
- Jar capacity: [tex]\(2 \frac{1}{4} = 2 + \frac{1}{4} = \frac{8}{4} + \frac{1}{4} = \frac{9}{4} \, \text{l}\)[/tex]
3. Determine the number of jars that can be filled:
- Number of jars = Total tank capacity / Capacity of one jar
- Number of jars = [tex]\( \frac{\frac{225}{8}}{\frac{9}{4}} = \frac{225}{8} \times \frac{4}{9} = \frac{225 \times 4}{8 \times 9} = \frac{900}{72} = 12.5 \, \text{jars} \)[/tex]
Thus, the cost for [tex]\(3 \frac{3}{4} \, \text{kg}\)[/tex] of tomatoes is [tex]\(₹88.295 \approx ₹88.30 \)[/tex], and the number of jars that can be filled from the tank is [tex]\(12.5\)[/tex].
### Problem 1: Finding the cost of [tex]\(3 \frac{3}{4} \, \text{kg}\)[/tex] of tomatoes
1. Understand the given values:
- The cost of [tex]\(8 \frac{1}{4} \; \text{kg}\)[/tex] of tomatoes is [tex]\(₹ 194 \frac{1}{4}\)[/tex].
2. Convert mixed numbers to improper fractions for easier calculations:
- [tex]\(8 \frac{1}{4} = 8 + \frac{1}{4} = \frac{32}{4} + \frac{1}{4} = \frac{33}{4} \, \text{kg}\)[/tex]
- [tex]\(194 \frac{1}{4} = 194 + \frac{1}{4} = \frac{776}{4} + \frac{1}{4} = \frac{777}{4} \, ₹\)[/tex]
3. Find the cost per kilogram:
- Cost per kg = Total cost / Total weight
- Cost per kg = [tex]\( \frac{\frac{777}{4}}{\frac{33}{4}} = \frac{777}{33} = 23.5454545454545 \, ₹/ \; \text{kg} \)[/tex]
4. Calculate the cost for [tex]\(3 \frac{3}{4} \, \text{kg}\)[/tex]:
- Convert [tex]\(3 \frac{3}{4}\)[/tex] to an improper fraction:
[tex]\(3 \frac{3}{4} = 3 + \frac{3}{4} = \frac{12}{4} + \frac{3}{4} = \frac{15}{4} \, \text{kg}\)[/tex]
- Total cost = Cost per kg [tex]\(*\)[/tex] weight in kg
- Total cost = [tex]\( 23.5454545454545 \times \frac{15}{4} = 88.2954545454545 \, ₹ \)[/tex]
### Problem 2: Finding how many jars each of capacity [tex]\(2 \frac{1}{4} \, \text{l}\)[/tex] can be filled from a tank of [tex]\(28 \frac{1}{8} \, \text{l}\)[/tex]
1. Understand the given values:
- Tank capacity: [tex]\(28 \frac{1}{8} \, \text{l}\)[/tex]
- Jar capacity: [tex]\(2 \frac{1}{4} \, \text{l}\)[/tex]
2. Convert mixed numbers to improper fractions for easier calculations:
- Tank capacity: [tex]\(28 \frac{1}{8} = 28 + \frac{1}{8} = \frac{224}{8} + \frac{1}{8} = \frac{225}{8} \, \text{l}\)[/tex]
- Jar capacity: [tex]\(2 \frac{1}{4} = 2 + \frac{1}{4} = \frac{8}{4} + \frac{1}{4} = \frac{9}{4} \, \text{l}\)[/tex]
3. Determine the number of jars that can be filled:
- Number of jars = Total tank capacity / Capacity of one jar
- Number of jars = [tex]\( \frac{\frac{225}{8}}{\frac{9}{4}} = \frac{225}{8} \times \frac{4}{9} = \frac{225 \times 4}{8 \times 9} = \frac{900}{72} = 12.5 \, \text{jars} \)[/tex]
Thus, the cost for [tex]\(3 \frac{3}{4} \, \text{kg}\)[/tex] of tomatoes is [tex]\(₹88.295 \approx ₹88.30 \)[/tex], and the number of jars that can be filled from the tank is [tex]\(12.5\)[/tex].
We hope this information was helpful. Feel free to return anytime for more answers to your questions and concerns. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.
