High School

Resuelva las siguientes situaciones:

a. María compró [tex]$\frac{1}{2}$[/tex] kilo de azúcar, [tex]$3 \frac{1}{2}$[/tex] kilos de frijoles, y [tex]$\frac{1}{4}$[/tex] kilo de otro producto. ¿Cabe todo lo que compró en una bolsa que resiste una masa de 5 kg?

Answer :

Sure! Let's go through the solution step-by-step:

1. Determine the Mass of Items Purchased:
- María bought [tex]\(\frac{1}{2}\)[/tex] kilo of sugar.
- She also bought [tex]\(3 \frac{1}{2}\)[/tex] kilos of beans. Converting the mixed number to an improper fraction gives us [tex]\(3 + \frac{1}{2} = 3.5\)[/tex] kilos.
- Therefore, the total mass of sugar and beans together is:
[tex]\[
\frac{1}{2} + 3.5 = 4.0 \text{ kilos}
\][/tex]

2. Calculate the Additional Fractional Mass:
- María also bought an additional [tex]\(\frac{1}{4}\)[/tex] of what she already has. To find this mass:
[tex]\[
\frac{1}{4} \times 4.0 = 1.0 \text{ kilo}
\][/tex]

3. Determine the Overall Mass:
- The total mass including the additional [tex]\(\frac{1}{4}\)[/tex] is:
[tex]\[
4.0 + 1.0 = 5.0 \text{ kilos}
\][/tex]

4. Assess the Capacity of the Bag:
- The bag can hold up to 5 kilos. Since the overall mass is exactly 5.0 kilos, it does not exceed the bag's capacity.

Therefore, María’s purchases do fit into the bag, as the total mass is exactly 5 kilograms, which the bag can handle.

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