Answer :
Let's solve the problem step by step.
1. Understanding the Purchase:
- María bought:
- [tex]\( \frac{1}{2} \)[/tex] kilo of sugar
- [tex]\( 3 \frac{1}{2} \)[/tex] kilos of beans
- [tex]\( \frac{1}{4} \)[/tex] kilo of coffee
2. Converting the Mixed Number:
- The weight of beans is given as a mixed number: [tex]\( 3 \frac{1}{2} \)[/tex].
- Convert this to an improper fraction or a decimal:
- [tex]\( 3 \frac{1}{2} = 3 + \frac{1}{2} = \frac{6}{2} + \frac{1}{2} = \frac{7}{2} = 3.5 \)[/tex] kilos
3. Calculating Total Weight:
- Add up all the weights to find the total:
- Total weight = sugar weight + beans weight + coffee weight
- Total weight = [tex]\( \frac{1}{2} + 3.5 + \frac{1}{4} \)[/tex]
4. Finding a Common Denominator:
- Convert all fractions to have a common denominator to easily sum them:
- [tex]\( \frac{1}{2} = \frac{2}{4} \)[/tex]
- [tex]\( 3.5 = \frac{7}{2} = \frac{14}{4} \)[/tex]
- [tex]\( \frac{1}{4} \)[/tex] is already with a denominator of 4
5. Calculate Total Weight with Common Denominator:
- Total weight = [tex]\( \frac{2}{4} + \frac{14}{4} + \frac{1}{4} = \frac{17}{4} \)[/tex]
6. Convert Total to Decimal:
- [tex]\( \frac{17}{4} = 4.25 \)[/tex] kg
7. Checking Bag Capacity:
- The bag can hold a maximum of 5 kg.
- Compare total weight with the bag's capacity:
- Total weight (4.25 kg) is less than 5 kg.
8. Conclusion:
- Yes, María can transport all her purchases in the bag, as the total weight is 4.25 kg, which is within the 5 kg limit.
1. Understanding the Purchase:
- María bought:
- [tex]\( \frac{1}{2} \)[/tex] kilo of sugar
- [tex]\( 3 \frac{1}{2} \)[/tex] kilos of beans
- [tex]\( \frac{1}{4} \)[/tex] kilo of coffee
2. Converting the Mixed Number:
- The weight of beans is given as a mixed number: [tex]\( 3 \frac{1}{2} \)[/tex].
- Convert this to an improper fraction or a decimal:
- [tex]\( 3 \frac{1}{2} = 3 + \frac{1}{2} = \frac{6}{2} + \frac{1}{2} = \frac{7}{2} = 3.5 \)[/tex] kilos
3. Calculating Total Weight:
- Add up all the weights to find the total:
- Total weight = sugar weight + beans weight + coffee weight
- Total weight = [tex]\( \frac{1}{2} + 3.5 + \frac{1}{4} \)[/tex]
4. Finding a Common Denominator:
- Convert all fractions to have a common denominator to easily sum them:
- [tex]\( \frac{1}{2} = \frac{2}{4} \)[/tex]
- [tex]\( 3.5 = \frac{7}{2} = \frac{14}{4} \)[/tex]
- [tex]\( \frac{1}{4} \)[/tex] is already with a denominator of 4
5. Calculate Total Weight with Common Denominator:
- Total weight = [tex]\( \frac{2}{4} + \frac{14}{4} + \frac{1}{4} = \frac{17}{4} \)[/tex]
6. Convert Total to Decimal:
- [tex]\( \frac{17}{4} = 4.25 \)[/tex] kg
7. Checking Bag Capacity:
- The bag can hold a maximum of 5 kg.
- Compare total weight with the bag's capacity:
- Total weight (4.25 kg) is less than 5 kg.
8. Conclusion:
- Yes, María can transport all her purchases in the bag, as the total weight is 4.25 kg, which is within the 5 kg limit.
