1. 1
   A fruit punch recipe uses juice, soda and lemonade in the ratio 20:30:40. A jug of the punch is made containing 180 ml in total.

   (a)

   Write the ratio 20:30:40 in its simplest form.

   [1 mark]

   • A1:2:2
   • B1:1.5:2
   • C4:6:8
   • D2:3:4

   (b)

   Using the simplest ratio, find the volume of juice in the 180 ml jug.

   [1 mark]

   • A20 ml
   • B40 ml
   • C60 ml
   • D80 ml

   (c)

   Find the ratio of soda to lemonade in its simplest form.

   [1 mark]

   • A2:3
   • B4:3
   • C3:4
   • D3:5

   Total for question 1: 3 marks

2. 2
   An inheritance of 60000 dollars is divided between two siblings in the ratio 5:7.

   (a)

   Find each sibling's share of the inheritance.

   [2 marks]

   (b)

   The elder sibling gives 15% of their share to charity. Find how much this is.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A map has a scale of 1:25000. Two towns are 8 cm apart on the map. Meanwhile, two juice bottles are sold: Bottle X, 750 ml for 3.00 dollars; Bottle Y, 1.2 litres for 4.32 dollars.

   (a)

   Find the actual distance between the two towns, giving your answer in km.

   [3 marks]

   (b)

   Determine which bottle offers better value, showing the cost per 100 ml for each.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   The cost, $C$ dollars, of hiring a coach is directly proportional to the number of passengers, $n$, when $n$ is below 40. For 25 passengers, the cost is 500 dollars. Separately, the time, $t$ hours, taken to build a wall is inversely proportional to the number of workers, $w$. It takes 8 workers 6 hours to build the wall.

   (a)

   Find the formula connecting $C$ and $n$, and use it to find the cost for 34 passengers.

   [4 marks]

   (b)

   Find the formula connecting $t$ and $w$, and use it to find how long it would take 12 workers to build the same wall.

   [4 marks]

   (c)

   A double-sized wall is now being built, so the time taken is directly proportional to the size of the wall as well as inversely proportional to the number of workers, meaning the proportionality constant found in part (b) doubles. Find the time taken for 16 workers to build this double-sized wall.

   [5 marks]

   Total for question 4: 13 marks

End of questions