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Sagot :
Let's solve each part of the word problems step-by-step:
### Part a:
Problem:
A milk bottle contains [tex]\( 1 \frac{1}{2} \)[/tex] liters of milk. How much milk will 15 such bottles contain?
Solution:
1. Convert the mixed number to an improper fraction:
[tex]\[ 1 \frac{1}{2} = 1 + \frac{1}{2} = \frac{2}{2} + \frac{1}{2} = \frac{3}{2} \][/tex]
2. Multiply the amount of milk in one bottle by the number of bottles:
[tex]\[ \frac{3}{2} \times 15 = 22.5 \][/tex]
So, 15 such milk bottles will contain [tex]\( 22.5 \)[/tex] liters of milk.
### Part b:
Problem:
One shirt requires [tex]\( 2 \frac{1}{4} \)[/tex] meters of cloth. How much cloth is required for 28 such shirts?
Solution:
1. Convert the mixed number to an improper fraction:
[tex]\[ 2 \frac{1}{4} = 2 + \frac{1}{4} = \frac{8}{4} + \frac{1}{4} = \frac{9}{4} \][/tex]
2. Multiply the amount of cloth required for one shirt by the number of shirts:
[tex]\[ \frac{9}{4} \times 28 = 63.0 \][/tex]
So, 28 such shirts will require [tex]\( 63.0 \)[/tex] meters of cloth.
### Part c:
Problem:
Shobhit's car covers [tex]\( 18 \frac{1}{2} \)[/tex] kilometers in one liter of petrol. How many kilometers will it cover in [tex]\( 8 \frac{1}{4} \)[/tex] liters?
Solution:
1. Convert the mixed numbers to improper fractions:
[tex]\[ 18 \frac{1}{2} = 18 + \frac{1}{2} = \frac{36}{2} + \frac{1}{2} = \frac{37}{2} \][/tex]
[tex]\[ 8 \frac{1}{4} = 8 + \frac{1}{4} = \frac{32}{4} + \frac{1}{4} = \frac{33}{4} \][/tex]
2. Multiply the distance covered per liter by the number of liters:
[tex]\[ \frac{37}{2} \times \frac{33}{4} = 152.625 \][/tex]
So, Shobhit's car will cover [tex]\( 152.625 \)[/tex] kilometers in [tex]\( 8 \frac{1}{4} \)[/tex] liters.
### Part d:
Problem:
Ritesh needs [tex]\( 14 \frac{1}{2} \)[/tex] dozens of bananas. If the cost of 1 dozen bananas is ₹ [tex]\( 5 \frac{1}{2} \)[/tex], how much money does Ritesh need to buy the bananas?
Solution:
1. Convert the mixed numbers to improper fractions:
[tex]\[ 14 \frac{1}{2} = 14 + \frac{1}{2} = \frac{28}{2} + \frac{1}{2} = \frac{29}{2} \][/tex]
[tex]\[ 5 \frac{1}{2} = 5 + \frac{1}{2} = \frac{10}{2} + \frac{1}{2} = \frac{11}{2} \][/tex]
2. Multiply the number of dozens needed by the cost per dozen:
[tex]\[ \frac{29}{2} \times \frac{11}{2} = 79.75 \][/tex]
So, Ritesh needs ₹ [tex]\( 79.75 \)[/tex] to buy [tex]\( 14 \frac{1}{2} \)[/tex] dozens of bananas.
### Part a:
Problem:
A milk bottle contains [tex]\( 1 \frac{1}{2} \)[/tex] liters of milk. How much milk will 15 such bottles contain?
Solution:
1. Convert the mixed number to an improper fraction:
[tex]\[ 1 \frac{1}{2} = 1 + \frac{1}{2} = \frac{2}{2} + \frac{1}{2} = \frac{3}{2} \][/tex]
2. Multiply the amount of milk in one bottle by the number of bottles:
[tex]\[ \frac{3}{2} \times 15 = 22.5 \][/tex]
So, 15 such milk bottles will contain [tex]\( 22.5 \)[/tex] liters of milk.
### Part b:
Problem:
One shirt requires [tex]\( 2 \frac{1}{4} \)[/tex] meters of cloth. How much cloth is required for 28 such shirts?
Solution:
1. Convert the mixed number to an improper fraction:
[tex]\[ 2 \frac{1}{4} = 2 + \frac{1}{4} = \frac{8}{4} + \frac{1}{4} = \frac{9}{4} \][/tex]
2. Multiply the amount of cloth required for one shirt by the number of shirts:
[tex]\[ \frac{9}{4} \times 28 = 63.0 \][/tex]
So, 28 such shirts will require [tex]\( 63.0 \)[/tex] meters of cloth.
### Part c:
Problem:
Shobhit's car covers [tex]\( 18 \frac{1}{2} \)[/tex] kilometers in one liter of petrol. How many kilometers will it cover in [tex]\( 8 \frac{1}{4} \)[/tex] liters?
Solution:
1. Convert the mixed numbers to improper fractions:
[tex]\[ 18 \frac{1}{2} = 18 + \frac{1}{2} = \frac{36}{2} + \frac{1}{2} = \frac{37}{2} \][/tex]
[tex]\[ 8 \frac{1}{4} = 8 + \frac{1}{4} = \frac{32}{4} + \frac{1}{4} = \frac{33}{4} \][/tex]
2. Multiply the distance covered per liter by the number of liters:
[tex]\[ \frac{37}{2} \times \frac{33}{4} = 152.625 \][/tex]
So, Shobhit's car will cover [tex]\( 152.625 \)[/tex] kilometers in [tex]\( 8 \frac{1}{4} \)[/tex] liters.
### Part d:
Problem:
Ritesh needs [tex]\( 14 \frac{1}{2} \)[/tex] dozens of bananas. If the cost of 1 dozen bananas is ₹ [tex]\( 5 \frac{1}{2} \)[/tex], how much money does Ritesh need to buy the bananas?
Solution:
1. Convert the mixed numbers to improper fractions:
[tex]\[ 14 \frac{1}{2} = 14 + \frac{1}{2} = \frac{28}{2} + \frac{1}{2} = \frac{29}{2} \][/tex]
[tex]\[ 5 \frac{1}{2} = 5 + \frac{1}{2} = \frac{10}{2} + \frac{1}{2} = \frac{11}{2} \][/tex]
2. Multiply the number of dozens needed by the cost per dozen:
[tex]\[ \frac{29}{2} \times \frac{11}{2} = 79.75 \][/tex]
So, Ritesh needs ₹ [tex]\( 79.75 \)[/tex] to buy [tex]\( 14 \frac{1}{2} \)[/tex] dozens of bananas.
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