3.04 Rates in context

It requires approximately 8 mL of polyethylene to create 20 plastic bags.

While filling a pool 72 centimetres deep, Victoria notices it has taken 3 hours to fill it up to a depth of 36 centimetres.

Skye is taking part in a hotdog eating competition. What compound units could be used to measure how quickly she can eat hotdogs?

A tap fills up a 240 litre tub in 4 hours.

A toy manufacturer makes 720 toys in 9 hours.

Justin earns \$420 in 6 hours. Write down Justin's hourly rate.

Tricia reads 20 pages of her book in 2 hours. Write down the unit rate of pages per hour.

Tina burns 640 calories by jogging 8 kilometres. Write down the rate at which Tina burns calories per kilometre?

A tap fills up a 98 Litre tub in 2 hours. What is the rate of water flow of the tap?

A car travels 253 kilometres on 11 litres of biofuel. Express the fuel consumption as a unit rate.

Write the following as a unit rate: Travel 429 kilometres in 6.5 hours

A film maker is stitching together frames for a movie. They put together 6 frames for every 0.2 seconds. What's the frame rate of the movie in frames per second?

Convert:

A crabeater seal can filter 0.9 litres of water in each dive while looking for food. They can stay under water for 30 minutes each dive.

A runner approximates the distance between two street lights to be 33 metres. It takes them 10 seconds to run from one street light to the other.

A pulse was recorded beating at 17 times per 15 seconds. How many beats per minute is this?

In an ice cream eating contest, the winner ate 2.22 litres of ice cream in 2 minutes.

What was the winner's rate of consumption of ice-cream in mL/s?

Two shearers wanted to work out who was the faster shearer. Jenny sheared 144 sheep over 6 days, and Sean sheared 115 sheep in 5 days.

Avril is running from John in a game of tag. Avril runs 30 metres every 5 seconds and John runs 21 metres every 3 seconds.

Tom's car can travel 5000 kilometres on 1260 litres of fuel. Susana's car can travel 1600 kilometres on 192 litres of fuel.

Who owns the most fuel efficient car?

A 1.5 kg crab costs \$24. What is the cost per kilogram?

Calculate the price per unit for the following, if:

Calculate the amount per dollar to two decimal places if you can buy:

Consider the following sales:

• 6 pencil cases for \$24 at Big Z.
• 9 pencil cases for \$54 at X-mart.

Which is cheaper: 148 mangos for \$384.80 at shop A or 252 mangos for \$453.60 at shop B?

There are three brands of bottled water in the market. Their prices are shown below:

• Brand A: 2 L for \$3.

• Brand B: 7L for \$11

• Brand C: 15 L for \$9

Determine which brand is:

Determine which shop offers the best buy:

A cafe sells coffees for \$4 each and offers one free coffee for every 6 coffees a customer buys.

How much more would a customer wanting to purchase 7 coffees have to pay if the special offer did not exist?

A carton of 10 eggs cost \$6.50. How much does 1 egg cost?

A 0.75 litre bottle of milk costs \$1.05. How much does the milk cost per litre?

A 1.35 kg packet of mince costs \$15. How many grams of mince does each dollar buy?

Iain feels like buying some ice-cream for himself and his friends. He considers the following offers:

• A box of 8 Cornettos costs \$18.00

• A box of 5 Magnums costs \$7.25

Isabelle is buying juice for her nephew's birthday party. She considers the following offers:

• A 3.2 L bottle of apple juice costs \$13.76

• A 2.1 L bottle of orange juice costs \$6.30

Which juice is the best buy?

Lisa has never made a potato salad before and wants to try making one. She has to choose between two types of potatoes at the store:

• A 10.275 kg sack of sebago potatoes costs \$13.70

• A 7.7 kg sack of russet potatoes costs \$14.00

Sally is deciding which of two different cereals she should buy:

• Choco Pops costs \$0.84 for 200 grams

• Special Q costs \$0.36 for 100 grams

A supermarket sells two different brands of eggs, Happy Hens and Sunny Side Up.

• Happy Hens eggs cost \$6.00 for 12 eggs

• Sunny Side Up eggs cost \$1.50 for 5 eggs

Barry's Bargain Bins sells backpacks for \$5.00 each, and if you buy 5 backpacks the 6th is free.

Lucie's Low Price Supplies sells backpacks for \$6.50 each, and if you buy 6 backpacks the 7th is free. Holly wants to buy 21 backpacks.

Which store should Holly shop at? Explain your answer.

Buzz bought 6 stamps for \$24. Find the price of:

Neil bought 18 stamps for \$198. Find the price of:

3.1 kg of pears cost \$7.13. How much would 1.5 kg cost?

4.2 kg of pears cost \$7.14. How many kilograms of pears can you purchase with \$6.46?

\$7.90 pays for 3 hours of parking. How long can you park for with \$15.80?

James needs 1 kg of blueberries to make a pie. He made a list of the prices of blueberries in four supermarkets close to his house:

• Market Fresh: 1 kg for \$3

• Garden Fresh: 500 g for \$2.25

• Fruit World: 2 kg for \$5.50

• My Market: 2 kg for \$6

Which shop was selling blueberries at the cheapest price per kilogram?

A direct factory outlet sells 40 L of detergent for \$694 to the public. Meanwhile, the local hardware store sells 8 L of the same detergent for \$92.

Calculate the discount in dollars per litre when buying from the hardware store, rather than the direct factory outlet.

Hairmart a wholesale hairdressing warehouse, sells 10 L bottles of shampoo for \$20. The same shampoo can be bought from retail stores at \$2 for 250 mL.

How much more expensive in dollars per litre is the shampoo when bought from the retail store?

James paid \$89 for 61 L of petrol in North Haverbrook. Valentina paid \$76 for 45 L of petrol in Dunkilderry.

James buys 28 L of petrol in Oklachusetts. How much will this cost if the petrol price matches the best price per litre between North Haverbrook and Dunkilderry?

At a grower’s market, durians are sold at Emporio for 56 cents per kilogram. At Greenery, each 4.5 kg durian is sold for \$3.50.

Consider the sale listings of two properties, the first property is a 350\text{ m}^{2} property priced at \$650\,000 and the second is a 459\text{ m}^{2} property listed for \$750\,000.

The price of a 200 square metre apartment originally selling for \$662\,000 is reduced by 2\%. The price of an adjacent apartment 240 square metres in size is \$675\,000.

A 500 g bag of almonds usually costs \$12.95 and a 200 g bag of almonds costs \$8.95. Today the 500 g bag is for sale at 10\% off.

2 L of milk, with an expiry date a week from today, costs \$3.00. A large 4 L bottle of the same brand, which expires in two days, is discounted to \$3.40.

Carol needs 2 planks of wood to complete a cabinet she is going to sell. The planks of wood are sold in packs of 3 for \$40 per pack or in a pack of 10 for \$100 per pack.

Explain when buying in bulk might not actually be worthwhile.