293 guests at convention, guests are centipedes and millipedes, centipedes have 14 legs, millipedes have 16 legs, total 4408 legs at convention, how many are ce

Question

293 guests at convention, guests are centipedes and millipedes, centipedes have 14 legs, millipedes have 16 legs, total 4408 legs at convention, how many are centipedes, how many are millipedes

 

have to solve with ICE method

Answer 1

After reading the entire problem, we can construct a table to organize all the different quantities.  These quantity include total number of guess, total number of legs of each type of guess, the number of centipedes and millipedes there are individually, etc.  Each of these quantities occupy a column on the graph.  Each row occupies a trial and error in the calculations that satisfy the problem conditions.  These trial and errors are number of centipedes and number of millipedes that satisfy the total number of legs and guess at convention.  We know by logic that these numbers must be positive.

 

 

Illustration (I):  Create the table using the info layed out and pick numbers for c and m.

 

 

 

 c             |         m          |         total legs = 4408       |      total guess = 293

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Calculate (C): This is a list of formulas used in the trial and error process when inputting numbers into the table.

 

Let c = number of centipedes
Let m = number of millipedes
14 legs per centipede = 14 × c
16 legs per millipede = 16 × m
Total legs = (14 × c) + (16 × m)
Total guess = c + m

 

 

       c      |         m          |         total legs = 4408       |      total guess = 293

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100                   193                        4488                                293

 

105                   188                        4478                                293

 

 

 

Notice that as we increase c and decrease m, the total legs decrease by the same amount.  By the pattern we have, we started with 4488 total legs and went down to 4478 total legs.  Keep on this pattern until we get to 4408 total legs.

 

 

115                  178                         4458

 

130                  163                         4428

 

140                  153                         4408

 

 

When we have 140 centipedes and 153 millipedes, the total number of legs at the convention is 4408.  The total number of guess is 293.

 

 

Explain (E): A summary of what went down.

 

I used the formulas to guide in plugging in the numbers.  Then I applied the multiples of 100 rule to pick numbers for the sum.  100 was my base number.  The number added to it to give me  sum of 293 was 193.  These two numbers determined my starting point.  Then I applied the number of legs to determine which guest type will have the greatest or least number.  Of course I had to flip-flop them to see which pair will get me closer to my goal of achieving 4408 legs in total while still maintaining a total of 293 guests.