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Students from a school formed four teams to collect cans for recycling during the months of April and May. A record of their efforts is shown below. Use the table to answer parts (a) and (b).



\begin{table}

\captionsetup{labelformat=empty}

\caption{Number of Pounds Collected}


Team 1Team 2Team 3Team 4

April		$29 \frac{3}{4}$$33 \frac{7}{8}$$29 \frac{1}{2}$$36 \frac{3}{16}$

May		$35 \frac{1}{3}$$30 \frac{5}{12}$$27 \frac{3}{4}$$43 \frac{1}{2}$




\end{table}


AWhich team collected the most for the 2-month period? How much did they collect?


BWhat was the difference between the total pounds collected in April and the total pounds collected in May?

Verified Answer :

  • Team 4 collected the most, with a total of \(79 \frac{11}{16}\) lb.
  • The total weight collected in April was \(129 \frac{5}{16}\) lb.
  • The total weight collected in May was \(137\) lb.
  • The difference between May and April collections is \(\boxed{7 \frac{11}{16}}\) lb.

Explanation

  1. Calculate Team Totals and Identify the Maximum

First, calculate the total weight of cans collected by each team for the two-month period by adding the amounts from April and May.

Team 1: \(29 \frac{3}{4} + 35 \frac{1}{3} = (29+35) + (\frac{9}{12} + \frac{4}{12}) = 64 + \frac{13}{12} = 65 \frac{1}{12}\) lb.
Team 2: \(33 \frac{7}{8} + 30 \frac{5}{12} = (33+30) + (\frac{21}{24} + \frac{10}{24}) = 63 + \frac{31}{24} = 64 \frac{7}{24}\) lb.
Team 3: \(29 \frac{1}{2} + 27 \frac{3}{4} = (29+27) + (\frac{2}{4} + \frac{3}{4}) = 56 + \frac{5}{4} = 57 \frac{1}{4}\) lb.
Team 4: \(36 \frac{3}{16} + 43 \frac{1}{2} = (36+43) + (\frac{3}{16} + \frac{8}{16}) = 79 \frac{11}{16}\) lb.

Comparing these totals: \(79 \frac{11}{16} > 65 \frac{1}{12} > 64 \frac{7}{24} > 57 \frac{1}{4}\).
Thus, Team 4 collected the most, with a total of \(79 \frac{11}{16}\) lb.

  1. Calculate Total Differences Between Months

Next, calculate the total weight collected in April and the total weight collected in May, then find the difference between them.

Total April collection:
\(29 \frac{3}{4} + 33 \frac{7}{8} + 29 \frac{1}{2} + 36 \frac{3}{16} = (29+33+29+36) + (\frac{12}{16} + \frac{14}{16} + \frac{8}{16} + \frac{3}{16}) = 127 + \frac{37}{16} = 127 + 2 \frac{5}{16} = 129 \frac{5}{16}\) lb.

Total May collection:
\(35 \frac{1}{3} + 30 \frac{5}{12} + 27 \frac{3}{4} + 43 \frac{1}{2} = (35+30+27+43) + (\frac{4}{12} + \frac{5}{12} + \frac{9}{12} + \frac{6}{12}) = 135 + \frac{24}{12} = 135 + 2 = 137\) lb.

Difference:
\(137 - 129 \frac{5}{16} = 7 \frac{11}{16}\) lb.

  1. Summary of Results

The final results show that Team 4 collected the most with \(79 \frac{11}{16}\) lb, and the difference in total collection between May and April is \(7 \frac{11}{16}\) lb.

ATeam 4 collected \(79 \frac{11}{16}\) lb.
BThe difference is \(7 \frac{11}{16}\) lb.

Examples

Understanding how to sum and compare mixed numbers is essential for managing resources or inventory. For example, if you manage different warehouse locations, you can use these methods to track total shipments received over several months to identify which location is the most active or to monitor changes in overall productivity between different seasons. Accurate calculations ensure that you can make data-driven decisions regarding resource allocation.

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