2000019201

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Project ID: 
2000019201
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People in Kocourkov pay by coins named groschen. Their coins are worth 1, 5 or 7 groschen. Martin and Petr, who live in Kocourkov, emptied their saving boxes and started counting their saved coins. They found out that Petr had 6 pieces of each type of a coin more than Martin, who had 40 coins in total. They were surprised to find out that Martin has the same number of 1-groschen and 7-groschen coins in total as Petr has of 5-groschen ones. Petr was proud to have 78 groschen more than Martin, who was only 2 short of having 200 groschen. Which of the following systems can be used to find out how many coins of each type both boys have?
x+5y+7z=198xy+z=6x+y+z=40
x+5y+7z=198xy+z=6(x+6)+5(y+6)+7(z+6)=276
x+5y+7z=198x+yz=6(x+6)+5(y+6)+7(z+6)=276
x+5y+7z=202xy+z=6(x+6)+(y+6)+(z+6)=58
x+5y+7z=198xy+z=6x+5y+7z=40
x+5y+7z=198xy+z=6(x6)+5(y6)+7(z6)=276