Question

Given the following clues, can you work out the number of gold, silver and bronze medals that France, Italy and Japan got in this international sports competition?

Japan has 1 more gold medal, but 3 fewer silver medals, than Italy.

France has the most bronze medals (18), but fewest gold medals (7).

Each country has at least 6 medals of each type. Italy has 27 medals in total
. Italy has 2 more bronze medals than gold medals.
The three countries have 38 bronze medals in total.
France has twice as many silver medals as Italy has gold medals.

Answer 1

Answer:

Italy: 10 bronzes 9 silvers 8 golds

Japan: 10 bronzes 6 silvers 9 golds

France: 18 bronzes 16 silvers 7 golds

Step-by-step explanation:

There are 38 bronze medals in total for the 3 countries. France has 18 of them, so there are 20 bronze medals between Italy and Japan. These are the possible combinations, needing to be over 6:

Italy: either 6, 7, 8, 9, 10, 11, 12 , 13 or 14 bronze

Japan: 14, 13, 12, 11, 10, 9, 8, 7 or 6 bronze

Italy must have at least 8 gold, because they have more than France (who have 7). So, they need to have at least 10 bronzes as they have 2 more bronzes than golds. This means that Italy has at most 9 silvers.

Japan has at most 10 bronzes because there are 20 bronzes between Japan and Italy. They have one more gold than Italy, giving Japan at least 9 golds. Japan also have 3 less silvers than Italy, giving them at most 6 silvers. France has twice as many silvers as Italy has golds (8x2 = 16), so France has at least 16 silvers.

Now let's explore the possibilities for Italy's bronze medals. Italy can have 10, 11, 12, 13 or 14 bronzes. But if Italy has 11 or more bronzes, then it has 9 or more golds, and so it has at most 7 silvers. This means that Japan has at most 4 silvers, which isn't allowed. So Italy must have 10 bronzes exactly.

Answer 2

Given : clues, about number of gold, silver and bronze medals that France, Italy and Japan got in this international sports competition

To find :  Each country medal tally

Solution:

Each country has at least 6 medals of each type.

France has 18 bronze medal

The three countries have 38 bronze medals in total.

=> Italy + Japan has 38 - 18 = 20 Bronze medals

Italy has 2 more bronze medals than gold medals. so Italy has minimum 8 bronze medals

Let say Italy Has    8 + B bronze medal   Then   Japan has 20 - (8 + B) =  12 - B  bronze medal

B lies between 0 & 6  

Italy has gold medal = 6 + B  

Italy total medal = 27

Italy Silver Medal  = 27 - (8 + B) - (6 + B)  = 13  - 2B

13  - 2B  > 6

=> B lies between 0  & 3

Japan Gold medal = 6 + B + 1 = 7 + B

Japan has Silver medals =  13 - 2B - 3  = 10  - 2B

=> B = 0 , 1 or 2  only possible

Italy has gold medal = 6 + B  

France has  fewest gold medal  = 7

=> 6 + B > 7

=> B > 1

Hence only possible value of B = 2

Italy gold medal = 6 + 2 = 8

Italy Bronze medal = 8 + 2 = 10

italy Silver medal = 13 - 2B  =  9

Japan gold medal = 7 + 2  = 9

Japan Silver Medal = 9 - 3 = 6   or 10 - 2B =  6

Japan Bronze model = 12 - B = 12  - 2 = 10

France Bronze medal = 18

France silver medal = 2 x 8  = 16

France gold medals  = 7

                         

                         GOLD        SILVER         BRONZE

JAPAN                   9                  6                   10

ITALY                     8                  9                   10

FRANCE                 7                 16                   18

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