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A class collected 2,650L of materials to recycle. Reginald said that 2,650÷49(1)/(10) could represent the volume of each bag if the class filled 49(1)/(10) bags with material to recycle. Peni said that 2,650÷49(1)/(10) could represent the number of containers the class filled if each container holds 49(1)/(10)L of material. Whose interpretation makes sense in this context? Choose 1 answer: A Reginald's only (B) Peni's only (c) Both Reginald's and Peni's

A class collected 2,650 L 2,650 \mathrm{~L} of materials to recycle.\newlineReginald said that 2,650÷49110 2,650 \div 49 \frac{1}{10} could represent the volume of each bag if the class filled 49110 49 \frac{1}{10} bags with material to recycle.\newlinePeni said that 2,650÷49110 2,650 \div 49 \frac{1}{10} could represent the number of containers the class filled if each container holds 49110 L 49 \frac{1}{10} \mathrm{~L} of material.\newlineWhose interpretation makes sense in this context?\newlineChoose 11 answer:\newline(A) Reginald's only\newline(B) Peni's only\newline(C) Both Reginald's and Peni's

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Q. A class collected 2,650 L 2,650 \mathrm{~L} of materials to recycle.\newlineReginald said that 2,650÷49110 2,650 \div 49 \frac{1}{10} could represent the volume of each bag if the class filled 49110 49 \frac{1}{10} bags with material to recycle.\newlinePeni said that 2,650÷49110 2,650 \div 49 \frac{1}{10} could represent the number of containers the class filled if each container holds 49110 L 49 \frac{1}{10} \mathrm{~L} of material.\newlineWhose interpretation makes sense in this context?\newlineChoose 11 answer:\newline(A) Reginald's only\newline(B) Peni's only\newline(C) Both Reginald's and Peni's
  1. Understand the problem: Understand the problem.\newlineWe need to determine if the division 2,650÷49(110)2,650\div49\left(\frac{1}{10}\right) represents the volume of each bag (as per Reginald's interpretation) or the number of containers filled (as per Peni's interpretation).
  2. Convert to improper fraction: Convert the mixed number 4911049\frac{1}{10} to an improper fraction.49110=49+110=49×10+110=4911049\frac{1}{10} = 49 + \frac{1}{10} = \frac{49\times 10 + 1}{10} = \frac{491}{10}
  3. Perform division calculation: Perform the division to find out what 2,650÷49(110)2,650\div49\left(\frac{1}{10}\right) equals.\newline2,650÷491/10=2,650×10/491=26,500/4912,650 \div 491/10 = 2,650 \times 10/491 = 26,500/491
  4. Simplify fraction: Simplify the fraction 26,500491\frac{26,500}{491} to find the exact value.\newline26,500491\frac{26,500}{491} is a division that can be performed to get a decimal value, but for the context of the problem, we don't need to calculate the exact decimal. We just need to understand what the result represents.
  5. Interpret the result: Interpret the result in the context of the problem.\newlineIf we divide the total volume of materials (2,650 L2,650\,\text{L}) by the volume of each bag (49110 L49\frac{1}{10}\,\text{L}), we get the number of bags needed to hold all the materials. This is Peni's interpretation.\newlineIf we divide the total volume of materials (2,650 L2,650\,\text{L}) by the number of bags (4911049\frac{1}{10}), we would be trying to find the volume of each bag, which doesn't make sense because the number of bags is not a volume. This is Reginald's interpretation.
  6. Determine correct interpretation: Determine whose interpretation is correct.\newlinePeni's interpretation makes sense because it gives us the number of containers needed to hold a certain volume of material. Reginald's interpretation does not make sense because the number of bags is not a measure of volume.

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