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Mathematics
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Oct 14th, 2014

1.              red = 3  black = 4

      then    red = x     black = 80

Now             3 : 4 : : x : 80

                     3 / 4 = x / 80

                     80 * 3 / 4 = x

                     x = 240/4

                     x = 60

Hence if there are 80 black then there are 60 red.

2.  a.                 5 min and 15 seconds = 5 minutes + 15/60 minutes

                                                         = 5 minutes  + 0.25 minutes

                                                         = 5.25 minutes

b.                     1 min = 2000 gallons

      Now           5.25 * 1 min = 5.25 * 2000 gallons

                        5.25 minutes = 10500 gallons

3. a.                1 : 84 means that 1 unit of length on the model represents 84 of the same unit of length on the real                             thing so the model is 1/84 the size of the real thing → and the scale factor is 1/84

b.                    tall ship model length = 103.2

      then          1 : 84 : : 103.2 cm : x

                          1/84 = 103.2/x

                           84 = x/103.2

                           x = 84 * 103.2

                           x = 8668.8 cm

Hence the actual ship has the length of 8668.8 cm.

c.                    beam of actual ship = 10.97 m = 10.97 * 100 cm = 1097 cm

    now            beam of model ship = 1097 * 1/84

                       beam of model ship = 13.06 cm

Oct 14th, 2014

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