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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].
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