Best buys
To determine which item is better value, we need to find a common amount to compare. Often it's easiest 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. We can also compare the amount per dollar, where we work out how much of something we would get for one dollar. Everyone loves a great deal or a sale when they're shopping! However, most products today come in different varieties and are sold at more than one store.
Amount per unit
Are you better off paying $\$10.50$$10.50 for $3$3 kg of apples or $\$6.20$$6.20 for $2$2 kg of apples? An easy way to compare the two options is to find the price per kilogram for each option.
| $\$10.50$$10.50 for $3$3 kg | $\$6.20$$6.20 for $2$2 kg |
|---|---|
| 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$$6.20 for $2$2 kg of apples because it's a cheaper price per kilogram.
Amount per dollar
If David's deli sells $620$620 grams of salmon for $\$18$$18 and Fred's fish market sells $460$460 grams of salmon for $\$13$$13, if the fish is of similar quality, which is better value? Let's see how much salmon we would get for one dollar at each shop.
David's:
| Amount per dollar | $=$= | $\frac{620}{18}$62018 grams per dollar |
Expressing the rate as the amount of grams per dollar. |
| $=$= | $34.\overline{4}$34.4 grams per dollar |
Expressing the rate as a decimal. |
So at David's, we'd get approximately $34.4$34.4 grams of salmon for a dollar.
Fred's:
| Amount per dollar | $=$= | $\frac{460}{13}$46013 grams per dollar |
Expressing the rate as the amount of grams per dollar. |
| $\approx$≈ | $35.4$35.4 grams per dollar |
Expressing the rate as a decimal. |
We get approximately $35.4$35.4 grams of salmon at Fred's, which is slightly better value than at David's.
Worked example
example 1
At a growers' market, durians are sold at stand A for $80c$80c per kilogram. At stand B, each $4.5$4.5 kg durian is sold for $\$4.00$$4.00.
(a) First, calculate the price of $4.5$4.5 kg of durian from store A. Round your answer to two decimal places.
Think: How do we change the price per kilogram to work out the price for $4.5$4.5 kg?
Do: $4.5\times0.8=\$3.60$4.5×0.8=$3.60
(b) Which store is the best buy?
Think: In other words, at which store would you pay less for $4.5$4.5 kg of durian?
Do: Choose Store A, as you pay less for a $4.5$4.5 kg in this store.
(c) What should the owner of store C charge for his $4.5$4.5 kg durians if he wants to beat the best buy by $6%$6%. Round your answer to two decimal places.
Think: This means he wants to charge $94%$94% of the lowest price.
Do:
| $0.94\times3.60$0.94×3.60 | $=$= | $3.384$3.384 |
Finding $94%$94% of the price of $4.5$4.5 kg of durian. |
| $=$= | $\$3.38$$3.38 (to $2$2 d.p.) |
The owner of store C should charge $\$3.38$$3.38 for his $4.5$4.5 kg durians.
Practice questions
question 1
Calculate the amount per dollar to two decimal places if you can buy:
$349$349 g for $\$9$$9
$709$709 mL for $\$5$$5
$27$27 m for $\$15$$15
question 2
A direct factory outlet sells $40$40 L of detergent for $\$694$$694 to the public. Meanwhile, the local hardware store sells $8$8 L of the same detergent for $\$92$$92.
Calculate the discount in dollars per litre when buying from the hardware store rather than the direct factory outlet.
Give your answer correct to the nearest cent.
Other contexts
The truth is, rates are used in a variety of places in households (rates of cordials), agriculture (fertilisers and seeds), travel (speeds, entrance fees, fuel economy), business management (flow of customers) and the list goes on.
Let's look at some examples.
Practice questions
Question 3
What is the time required for a car to travel $170$170 kilometres at a speed of $10$10 kilometres per hour?
Question 4
In $2011$2011, the literacy rate in Cuba was $98$98 people for every $100$100 in the population. This is the rate of the population aged $15$15 and above who can, with understanding, read and write a short, simple statement on their everyday life. For a town with a population of $83000$83000, how many literate people would you expect?
Question 5
James paid $\$89$$89 for $61$61 L of petrol in North Haverbrook. Valentina paid $\$76$$76 for $45$45 L of petrol in Dunkilderry.
How much does petrol cost per litre in North Haverbrook? Give your answer correct to the nearest cent.
How much does petrol cost per litre in Dunkilderry? Give your answer correct to the nearest cent.
In which suburb is petrol cheaper?
North Haverbrook
ADunkilderry
BJames pumps $28$28 L in Oklachusetts. Using your answers from parts (a) and (b), how much will this cost if the petrol price matches the best price between North Haverbrook and Dunkilderry?