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A shopkeeper sold 100 fruits (3 types). Apple was sold for 10 cents each,Banana 1 Euro each and Orange sold for 3 Euro each. The total amount collected for the 100 fruits was 100 Euros. How many fruits of each type were sold?
\n" ); document.write( "Let a = no. of apples, b = no. of banana, r = no. of oranges
\n" ); document.write( ":
\n" ); document.write( "Since Banana's & Organges are in Euros, the number of apples sold at .10 have to
\n" ); document.write( "be multiples of 10 in order for it to add up to 100 Euros.
\n" ); document.write( "I tried 30 apples without success, however with 40 apples:
\n" ); document.write( ":
\n" ); document.write( "The number of fruit equation
\n" ); document.write( "40 + b + r = 100
\n" ); document.write( "b + r = 100 - 40
\n" ); document.write( "b + r = 60
\n" ); document.write( ":
\n" ); document.write( "And the Euro amt equation
\n" ); document.write( ".10(40) + 1b + 3r = 100
\n" ); document.write( "4 + 1b + 3r = 100
\n" ); document.write( "b + 3r = 100 - 4
\n" ); document.write( "b + 3r = 96
\n" ); document.write( ":
\n" ); document.write( "Gives us two, 2 unknown equations, we can solve by elimination:
\n" ); document.write( "b + 3r = 96
\n" ); document.write( "b + r = 60
\n" ); document.write( "------------- subtract
\n" ); document.write( "0 + 2r = 36
\n" ); document.write( " r = 36/2
\n" ); document.write( " r = 18 oranges
\n" ); document.write( ":
\n" ); document.write( "Substitute 40 for a and 18 for r in the fruit quantity equaiton:
\n" ); document.write( "40 + b + 18 = 100
\n" ); document.write( "b = 100 - 58
\n" ); document.write( "b = 42 bananas
\n" ); document.write( ":
\n" ); document.write( "Check our solutions in the euro equation:
\n" ); document.write( ".10(40) + 1(42) + 3(18) =
\n" ); document.write( "4 + 42 + 54 = 100
\n" ); document.write( ":
\n" ); document.write( "Solution: 40 apples, 42 bananas and 18 oranges \n" ); document.write( "