For each problem, write a complete description of how you approached finding the solution, including things that you tried that were not successful Identify the strategy that worked for you Write any other comments or include picture diagrams that you used Three blocks of cheese weigh 650 kilograms, 680 kilograms, and 740 kilograms For the purpose of packing and to avoid waste, the cheese is to be cut into pieces of equal weight How much should each piece weigh if the total number of pieces is to be as small as possible A manufacturer wants to put 3 items into each package and then 2 packages in each box The packing supervisor wants to know whether the 67,986 items in stock will fill a whole number of boxes Check and prove whether this is true or not Prize winners for a giveaway program are to be determined as follows Envelopes for the first 500 entries will be numbered 1 through 500 and laid on a long table The first official will walk along the table, opening all the envelopes The second official will follow the first and close every even numbered envelope The third official will follow the second, reversing every third envelope by closing open envelopes and opening closed envelopes The fourth official will reverse every fourth envelope, and so on until 500 officials have walked along the table and reversed envelopes The envelopes that remain open after this procedure will be those of the contest winners What numbers were on the winning envelopes A mathematics teacher wishes to use groups of 5 and or 7 students for a class assignment When she tries to make assignments she notices that it cannot be done with the number of students she has However, if the number of students were any larger, the assignments could be made How many students has the teacher In a game of simplified football a touchdown results in 7 points and a field goal results in 3 points What is the largest game score for a team not possible What is the shortest length of cable that can be cut into either a whole number of 18 ft pieces or a whole number of 30 ft pieces

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For each problem, write a complete description of how you approached finding the solution, including things that you tried that were not successful. Identify the

For each problem, write a complete description of how you approached finding the solution, including things that you tried that were not successful. Identify the strategy that worked for you. Write any other comments or include picture/diagrams that you used.

Three blocks of cheese weigh 650 kilograms, 680 kilograms, and 740 kilograms. For the purpose of packing and to avoid waste, the cheese is to be cut into pieces of equal weight. How much should each piece weigh if the total number of pieces is to be as small as possible?
A manufacturer wants to put 3 items into each package and then 2 packages in each box. The packing supervisor wants to know whether the 67,986 items in stock will fill a whole number of boxes. Check and prove whether this is true or not.
Prize winners for a giveaway program are to be determined as follows: Envelopes for the first 500 entries will be numbered 1 through 500 and laid on a long table. The first official will walk along the table, opening all the envelopes. The second official will follow the first and close every even-numbered envelope. The third official will follow the second, reversing every third envelope by closing open envelopes and opening closed envelopes. The fourth official will reverse every fourth envelope, and so on until 500 officials have walked along the table and reversed envelopes. The envelopes that remain open after this procedure will be those of the contest winners. What numbers were on the winning envelopes?
A mathematics teacher wishes to use groups of 5 and/or 7 students for a class assignment. When she tries to make assignments she notices that it cannot be done with the number of students she has. However, if the number of students were any larger, the assignments could be made. How many students has the teacher?
In a game of simplified football a touchdown results in 7 points and a field goal results in 3 points. What is the largest game score for a team not possible?
What is the shortest length of cable that can be cut into either a whole number of 18-ft pieces or a whole number of 30-ft pieces?