Question:Find the average of £1.34, £4.16 and £5.81 

£1.34+£4.16+£5.81 = £11.31
The average=`(£11.31)/3`= £3.77

Question:Find the average of x+y, 2x+3y, 2x-2y and 3x-2y 

(x+y)+(2x+3y)+(2x-2y)+(3x-2y) = x+2x+2x+3x+y+3y-2y-2y = 8x
The average = `8x/4`= 2x

Question:I buy 8 kg of cooking apples at 10p per kg and 2 kg of eating apples at 15p per kg. Find the average cost of 1 kg of apples. 

8 kg at 10p per kg cost 80 new pence
2 kg at 15p per kg cost 30 new pence
Total cost of 10 kg is  110 new pence
The average cost per kg is `110/10` = 11p.

Question:A merchant blends two brands of tea costing 60 new pence per kg an d80 new pence per kg in ratio 3:1. What is the cost of 1 kg of the mixture? 

Suppose he mixes 3 kg of 60p tea with 1 kg of 80p tea.
   Cost of 3 kg at 60p per kg is       180 new pence
   Cost of 1 kg at 80p per kg is         80 new pence
   Total cost of 4 kg of tea is         260 new pence
Average cost per kg is 65 new pence.

Question:A boy cycles 10 km at 15 km/h and a further 20 km at 20 km/h. Find his average speed over the whole journey. 

The time taken to go d k at v km/h. = `d/v` hours.

The time taken to cycle 10 km at 15 km/h. = `10/15` = `2/3` hour.

The time taken to cycle 20 km at 20 km/h. = `20/20` = 1 hour.

The total time taken to cycle 30 km = `1 2/3` hours.

The average speed = distance gone/time taken = `30/(1 2/3) = 90/5 = 18 km/h`

Question:A motor-cyclist mixes oil and petrol in the ratio 1:20. If petrol costs 9p per litre and oil 19 `1/2`p per litre, find the cost of a litre of the mixture. 

Consider any convenient volumes in the ratio 1:20, e.g 1 litre of oil and 20 litre of petrol.
  20 liters of petrol cost 20 x 9p = £1.80

  1 liters of oil costs 1 x 19`1/2`p = £`0.19 1/2`

  Total cost of 21 liters of mixture = £1.99`1/2`

Average cost per litre of mixture = `(£1.99 1/2)/21 = (199.1/2p)/21 = 9 1/2p`