3.03 Rates in context

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

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

Calculate the price per unit if:

A store sells hats for \$ 4 each and offers one free hat for every 6 hats a customer buys.

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.

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.

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.

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

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.

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 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.

Adam really likes apples and eats them at a rate of 4 per day.

Dave can wash 2 cars in 4 minutes.

Eileen can wash 7 plates in 28 minutes and lace 11 boots in 55 minutes.

There are 3 apartments per floor of a building. How many apartments are there over 8 floors?

In a library, there are 400 books per shelf. How many books are there in a row of 7 shelves?

The amount of pears that can fit in a plastic bag is 11 pears per bag. How many bags will be needed to carry 33 pears?

There are 224 tissues per box. If the manufacturer wastes 1120 tissues in production, how many boxes of tissues are wasted?

Calculate the distance travelled by the following vehicles:

Calculate time required for a person to jog 170 \text{ km} at a speed of 10 \text{ km/h}.

A worm takes 18 \text{ sec} to travel 25 \text{ cm}. How long does it take the worm to travel one metre?

The height of a pool increases by 5 \text{ cm} for every 10 \text{ L} of water added. After adding some water, the height of the pool increased by 0.45 \text{ m}.

The height of a pool increases by 0.9 \text{ cm} for every litre of water added. If the height of the pool increases by 54 \text{ cm}, how much water was added?

Iain earns \$22 per hour working as a performer. If Iain works for 20 hours a week, determine his weekly earnings.

Caitlin plays cricket over the summer holidays. Caitlin scores at rate of 24 runs per game and there are 30 games in the season. Calculate the total runs that Caitlin scored in the season.

The volume of polyethylene used to create 81 plastic bags is approximately 18 \text{ mL}. How much polyethylene would be required to create 9 plastic bags?

An industrial detergent requires 19 \text{ mL} of water to be added to every 1 \text{ mL} of the detergent for safe usage. How many litres of water must be added to 610 \text{ mL} of detergent?

In 2017, the literacy rate in Cuba was 98 people for every 100 in the population, while in Chad, it was 35 people for every 100 in the population. This is the rate of the population aged 15 and above who can, with understanding, read and write a short, simple statement on their everyday life.

How many literate people would you expect:

In 2018, Japan's birthrate was 9 people for every 1000 in the population, while Canada's birthrate was 11 people for every 1000 in the population.

Compute for the number of births expected in that year for the following towns, correct to one decimal place if necessary:

In 2019, the population growth of Papua New Guinea was 22 per 1000 while in Oman, the population growth was 91 per 1000. This means that for every 1000 people, the number of people at the end of the year would be 1022 in Papua New Guinea and 1091 in Oman.

Calculate the population at the end of the year for the following towns, rounded to the nearest integer.

Bianca keeps track of her fuel consumption over a month, and calculates that her motorcycle consumed 144 \text{ L} of fuel. Its fuel economy is listed as 10.6 \text{ km/L}. How many kilometres did she travel over the month?

Xanthe drives 20\,400 \text{ km} around the city each year and has a car with a fuel economy of 0.04 \text{ L/km}. How many litres of fuel does the car consume in a year?

A car travels 1650 \text{ km} to Uluru. The car has a fuel economy of 12.8 \text{ L/} 100 \text{ km}. How many litres will the car consume getting to Uluru?

Homer is driving 700 \text{ km} to visit his family. The car has a fuel economy of 5 \text{ L/} 100 \text{ km}. How many litres of fuel will Homer require to make this trip?

Harry owns a 4WD with a fuel efficiency of 8 \text{ L/} 100 \text{ km} which usually requires 126 \text{ L} of fuel per week. Harry also owns a sedan which has a fuel efficiency of 7 \text{ L/} 100 \text{ km} which usually requires 240 \text{ L} of fuel per week.

Amy has to travel 1450.4 \text{ km} for a camping trip. Her car has a fuel consumption rate of 8 \text{ km/L}.

Brendan wants to purchase a 4WD, and there are 2 models:

• A diesel 4WD which has a fuel efficiency of 6.3 \text{ L/} 100 \text{ km} and

• An unleaded petrol 4WD which has a fuel efficiency of 9.5 \text{ L/} 100 \text{ km}

Brendan drives approximately 25\,800 \text{ km/year}. On average, the price of unleaded petrol is 156.7 cent per litre, and for diesel it is 142.7 cent per litre.

Patricia is considering switching from using premium fuel to E10 in her car. The price of E10 petrol is, on average, 152 cents per litre, and for premium petrol it is 169 cents per litre.

According to the manufacturer's website her car's fuel efficiency using E10 petrol is 4.3 \text{ L/} 100 \text{ km}, while using premium petrol it is 3.9 \text{ L/} 100 \text{ km}.

Patricia drives approximately 17\,200 \text{ km/year}.

A new hybrid car uses only 50 \text{ mL} of fuel to travel 250 \text{ m} in test conditions. Robert is considering purchasing the hybrid car but wants to make sure it is more fuel efficient than his current car. He conducts his own test by recording how far he travels and how much fuel he uses over a month. The results were that he went 1447.6 \text{ km} and used 308 \text{ L} of fuel.

Yvonne wants to fill up her car's fuel tank. It has a capacity of 50 \text{ L} and currently has 9 \text{ L} of fuel in the tank.

The two closest petrol stations are OzPet, which has petrol for 153.7 cents and is 19 \text{ km} away, and DinoFuel, which has petrol for 144.3 cents and is 31 \text{ km} away.

Yvonne's car has a fuel efficiency of 0.03 \text{ L/km}.

Caitlin is replacing her V6 engine with a more fuel efficient four cylinder engine. To convert to the new engine will cost \$4400 up front, but will improve the rate of fuel consumption of the car from 11.6 \text{ L/} 100 \text{ km} to 8.4 \text{ L/} 100 \text{ km}. Caitlin travels 11\,400 \text{ km/year}.

Rochelle is moving house and needs to move some furniture. She found information about the efficiency of towing with her own car as shown in the table: