On a trip, a motorist purchased gasoline as follows: 58 litres at 128.7 cents per litre; 69 litres at 132.2 cents per litre; 71 litres at 122.6 cents per litre, and 56 litres at 133.4 cents per litre.
Round your final answers properly to two decimal places.
a) What is the average number of litres per purchase?
b) What was the average cost per litre?
____________ cents / L
c) If the motorist averaged 9.68 km per litre, what was the average cost of gasoline per kilometre?
____________ cents / km
a) The average amount per purchase is a simple average: The total amount of the purchases (58+69+71+56) divided by the total number of purchases (4). `(58+69+71+56)-:4=254-:4=63.50` Litres
b) The price per Litre of all the purchases is a weighted average. You find that by finding the combined prices and dividing by the combined Litres bought. You find the combined prices by multiplying the number of litres by its unit price. `(58 L)/1 xx (128.7 cents)/L=7,464.6 cents`
`(69L)/1 xx (132.2 cents)/L=9,121.8cents`
`(71 L)/1 xx (122.6 cents)/L=8,704.6cents`
`(56L)/1 xx (133.4 cents)/L=7,470.4cents`
Then we divide the total cents by the total Litres to find the average price per Litre
`(7,464.6+9,121.8+8,704.6+7,470.4)-:(58+69+71+56)=` `32,761.4-:254=128.98` cents/L
c) This is a simple conversion, cross cancelling units.
`(128.98 cents)/L xx (1L)/(9.68 km)=13.32`cents/km