Unit costs
Everyone loves a great deal or a sale when they're shopping! However, most products today come in different varieties or quantities and are sold at more than one store. 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.
Amount per unit
Are we 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 we'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$$13, and if the fish is of similar quality, which is better value? Let's see how much salmon we would get for one dollar at each shop.
David's:
| Amount per dollar | $=$= | $\frac{620}{18}$62018 grams per dollar |
Expressing the rate as the amount of grams per dollar |
| $=$= | $34.\overline{4}$34.4 grams per dollar |
Expressing the rate as a decimal |
So at David's, we'd get approximately $34.4$34.4 grams of salmon for a dollar.
Fred's:
| Amount per dollar | $=$= | $\frac{460}{13}$46013 grams per dollar |
Expressing the rate as the amount of grams per dollar |
| $\approx$≈ | $35.4$35.4 grams per dollar |
Expressing the rate as a decimal |
We get approximately $35.4$35.4 grams of salmon at Fred's, which is slightly better value than at David's.
Worked example
example 1
At a growers' market, pineapples are sold at stand A for $80c$80c per kilogram. At stand B, each $4.5$4.5 kg pineapple is sold for $\$4.00$$4.00.
(a) First, calculate the price of $4.5$4.5 kg of pineapple 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 has the lowest unit cost?
Think: In other words, at which store would you pay less for $4.5$4.5 kg of pineapple?
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 pineapples if he wants to beat the lowest unit cost 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 pineapple |
| $=$= | $\$3.38$$3.38 (to $2$2 d.p.) |
So the owner of store C should charge $\$3.38$$3.38 for his $4.5$4.5 kg pineapple.
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.
Question 3
Although cheaper, when might buying in bulk not actually be worth it? Select all that apply.
When the bulk items may expire before you get to use them all.
AWhen you actually only need a small amount.
BWhen your cash flow is tight and therefore you cannot spend more at the time even if it means you get the item at a lower unit price.
C