Comparing rates
Often we wish to compare rates to determine which item is better value. A common method is to find the unit price of each item, where we find the cost per unit of measurement, for example per litre, per kilogram or per item. To compare the fuel efficiency of cars we work out the number of kilometres per litre of petrol. We can also compare the amount per dollar, where we work out how much of something we would get for $\$1$$1.
Unit price
Worked example
Example 1
Are you better off paying $\$10.50$$10.50 for $3$3kg of apples or $\$6.20$$6.20 for $2$2kg of apples? An easy way to compare the two options is to find the price per kilogram for each option.
| $\$10.50$$10.50 for $3$3kg | $\$6.20$$6.20 for $2$2kg |
|---|---|
| Divide by $3$3 to get the price per kilo | Divide by $2$2 to get the price per kilo |
| $\$3.50$$3.50/kg | $\$3.10$$3.10/kg |
So you're better off paying $\$6.20$$6.20 for $2$2kg of apples because it's a cheaper price per kilogram.
Note: The rate is in $ per kg, think of this as "$ divided by kg". If we do the $ amount divided by the kg amount on the calculator we also get the same unit rate answer.
Amount per dollar
Example 2
If Bill's Brand sells $200$200 grams of cement for $\$24$$24 and Bob's Brand sells $150$150 grams of the same cement for $\$13$$13, which is better value? Let's see how much cement we would get for one dollar at each shop:
Bill's:
| $\$24$$24 | $=$= | $200$200 grams | (divide both sides by $24$24) |
| $\$1$$1 | $=$= | $8.33$8.33... grams |
So at Bill's, we'd get approximately $8.3$8.3 grams of cement for a dollar.
Bob's:
| $\$13$$13 | $=$= | $150$150 grams | (divide both sides by $13$13) |
| $\$1$$1 | $=$= | $11.53$11.53... grams |
We get approximately $11.5$11.5 grams of cement at Bob's, which is much better value than at Bill's.
Note: The rate is in grams per $, think of this as "grams divided by $". If we do the grams amount divided by the $ amount on the calculator we also get the same unit rate answer.
Practice questions
Question 1
Isabelle is buying juice for her nephew's birthday party.
A $3.2$3.2 L bottle of apple juice costs $\$13.76$$13.76.
A $2.1$2.1 L bottle of orange juice costs $\$6.30$$6.30.
How much does apple juice cost per litre?
How much does orange juice cost per litre?
Which juice is the best value?
Orange juice
AApple juice
B
Question 2
James needs $1$1 kg of blueberries to make a pie. He made a list of the prices of blueberries in four supermarkets close to his house.
| Shop | Price for blueberries |
|---|---|
| Market Fresh | $1$1 kg for $\$3$$3 |
| Garden Fresh | $500$500 g for $\$2.25$$2.25 |
| Fruit World | $2$2 kg for $\$5.50$$5.50 |
| My Market | $2$2 kg for $\$6$$6 |
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Which shop was selling blueberries at the cheapest price per kilogram?
Garden Fresh
AMarket Fresh
BMy Market
CFruit World
D
Fuel consumption per L and per 100 L
Fuel consumption can be written as a rate per litre, but is often more meaningful if written as a rate per $100$100 litres.
Worked example
Example 3
A car with a $60$60 L petrol tank can travel $540$540 km before it runs out of petrol. Calculate the rate of fuel consumption in L per $100$100 km.
Think: Calculate the number of litres per km by dividing the number of litres by the number of kilometres. Then multiply by $100$100 to find the number of litres per $100$100 km.
Do: Rate per km is $60\div540=0.1111$60÷540=0.1111L per km
Rate per $100$100 km is $0.1111\times100=11.11$0.1111×100=11.11L per $100$100 km
Practice questions
Question 3
Neville is deciding between four cars to buy. He wants to buy the most fuel efficient one.
Complete the table.
Car Litres used Distance travelled (km) L/km Magnum $13.405$13.405 $38.3$38.3 $\editable{}$ Falcador $20.71$20.71 $54.5$54.5 $\editable{}$ Canyonero $6.336$6.336 $19.2$19.2 $\editable{}$ Civil $2.754$2.754 $8.1$8.1 $\editable{}$ Which car is the most fuel efficient?
Civil
AMagnum
BCanyonero
CFalcador
D
Question 4
A car travels $80$80 kilometres and consumes $6.96$6.96 litres of fuel.
What is the rate of fuel consumption of the car in L/km? Give your answer as a decimal.
What is the rate of fuel consumption of the car in L/$100$100 km?