To determine how much water is still needed to fill the fish tank after Alejandro and Anthony have poured their amounts, let's solve this step-by-step.
1. Convert Mixed Numbers to Improper Fractions:
- Alejandro's water: [tex]\( 2 \frac{11}{15} \)[/tex]
[tex]\[
2 \frac{11}{15} = 2 + \frac{11}{15} = \frac{30}{15} + \frac{11}{15} = \frac{41}{15}
\][/tex]
- Anthony poured [tex]\( 1 \frac{3}{5} \)[/tex] liters less than Alejandro:
[tex]\[
1 \frac{3}{5} = 1 + \frac{3}{5} = \frac{5}{5} + \frac{3}{5} = \frac{8}{5}
\][/tex]
2. Convert [tex]\( \frac{8}{5} \)[/tex] to a common denominator of 15:
[tex]\[
\frac{8}{5} = \frac{8 \times 3}{5 \times 3} = \frac{24}{15}
\][/tex]
3. Determine Anthony's water, which is [tex]\( \frac{41}{15} - \frac{24}{15} \)[/tex]:
[tex]\[
\frac{41}{15} - \frac{24}{15} = \frac{41 - 24}{15} = \frac{17}{15}
\][/tex]
4. Calculate the total water poured into the tank:
- Alejandro: [tex]\( \frac{41}{15} \)[/tex]
- Anthony: [tex]\( \frac{17}{15} \)[/tex]
[tex]\[
\text{Total water poured} = \frac{41}{15} + \frac{17}{15} = \frac{41 + 17}{15} = \frac{58}{15}
\][/tex]
5. Convert the total capacity of the tank into an improper fraction:
- Tank capacity: 8 liters
[tex]\[
8 = \frac{8 \times 15}{15} = \frac{120}{15}
\][/tex]
6. Calculate the water still needed to fill the tank:
[tex]\[
\frac{120}{15} - \frac{58}{15} = \frac{120 - 58}{15} = \frac{62}{15}
\][/tex]
7. Convert [tex]\( \frac{62}{15} \)[/tex] to a mixed number:
[tex]\[
\frac{62}{15} = 4 \frac{2}{15}
\][/tex]
Therefore, the tank still needs [tex]\( 4 \frac{2}{15} \)[/tex] liters of water to be filled completely. The correct answer is:
b) [tex]\( 4 \frac{2}{15} \)[/tex]
