This weeks

Year 7 & 8 Middle and Upper Band Year 7 & 8 Fast Track Year 7 & 8 High Achievers Year 9 & 10 Middle and Upper Band Year 9 & 10 Fast Track Year 9 & 10 High Achievers

Year 7 & 8 Middle and Upper Band Partial Magic In a magic square, each row, each column and both main diagonals have the same total. In the partially completed magic square shown, what number should replace x? ANSWER The numbers along the leading diagonal total 58, which is therefore the sum of each row and each column. We can now calculate that the number to the left of 10 must be 20 and below that must be 7. Hence x=21

Packing Boxes Year 7 & 8 Fast track Harry, Christine and Betty are packing 36 boxes of chocolates. Harry and Christine would take 2 hours to pack the boxes; Harry and Betty would take 3 hours; Christine and Betty would take 4 hours. How many boxes does Christine pack in one hour? ANSWER In one hour, Harry and Christine together pack 18 boxes. Harry and Betty together pack 12 boxes. Christine and Betty together pack 9 boxes. Therefore Harry packs 3 more boxes than Christine, looking at the rates when they're each with Betty. In one hour Christine would therefore pack 7.5 boxes.

Alien Currency Year 7 & 8 High Achievers The currency used on the planet Zog consists of bank notes of a fixed size differing only in colour. Three green notes and eight blue notes are worth 46 zogs; eight green notes and three blue notes are worth 31 zogs. How many zogs are two green notes and three blue notes worth? ANSWER Let the value of a green note and the value of a blue note be g zogs and b zogs respectively. Then 3g+8b=46 and 8g+3b=31 . Adding these two equations gives 11g+11b=77 , so b+g=7 . Therefore 3g+3b=21 . Subtracting this equation from the original equations in turn gives 5b=25 and 5g=10 respectively. So b=5 , g=2 and 2g+3b=19

Packing Boxes Year 9 & 10 Middle and Upper Band Harry, Christine and Betty are packing 36 boxes of chocolates. Harry and Christine would take 2 hours to pack the boxes; Harry and Betty would take 3 hours; Christine and Betty would take 4 hours. How many boxes does Christine pack in one hour? ANSWER In one hour, Harry and Christine together pack 18 boxes. Harry and Betty together pack 12 boxes. Christine and Betty together pack 9 boxes. Therefore Harry packs 3 more boxes than Christine, looking at the rates when they're each with Betty. In one hour Christine would therefore pack 7.5 boxes.

Alien Currency Year 9 & 10 Fast Track The currency used on the planet Zog consists of bank notes of a fixed size differing only in colour. Three green notes and eight blue notes are worth 46 zogs; eight green notes and three blue notes are worth 31 zogs. How many zogs are two green notes and three blue notes worth? ANSWER Let the value of a green note and the value of a blue note be g zogs and b zogs respectively. Then 3g+8b=46 and 8g+3b=31 . Adding these two equations gives 11g+11b=77 , so b+g=7 . Therefore 3g+3b=21 . Subtracting this equation from the original equations in turn gives 5b=25 and 5g=10 respectively. So b=5 , g=2 and 2g+3b=19

Antifreeze Year 9 & 10 High Achievers A large container holds 14 litres of a solution that is 25% antifreeze, the remainder being water. How many litres of antifreeze must be added to the container to make a solution that is 30% antifreeze? ANSWER: 1 Let the extra volume of antifreeze required be x litres. Initially, there are 3.5 litres of antifreeze in the solution. So 3.5+x=0.3(14+x) , that is, 35+10x=42+3x , so x=1 .