For each of the following determine the price of one unit:
Three apples cost \$3.63
Twelve eggs cost \$3.84
Four pies cost \$21.00
Five hotdogs cost \$12.00
Consider the following sales:
- 6 pencil cases for \$24 at Big Z.
- 9 pencil cases for \$54 at X-mart.
What is the cost of a single pencil case at Big Z?
What is the cost of a single pencil case at X-mart?
Hence which is the best place to buy pencil cases, if you want the best price per item?
Consider the following prices of mangos:
148 mangos for \$384.80 at shop A, or
252 mangos for \$453.60 at shop B
What is the cost of a single mango at shop A?
What is the cost of a single mango at shop B?
Hence, which is the best place to buy mangos, if you want the best price per item?
Avril is running from John in a game of tag. Avril runs 30 \text{ m} every 5 \text{ sec} and John runs 21 \text{ m} every 3 \text{ sec}.
Calculate:
Avril's speed in metres per second.
John's speed in metres per second.
Who is faster? Avril or John?
2 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.
Calculate:
Jenny's rate in sheep per day.
Sean's rate in sheep per day.
If Jenny continued at this rate, how many sheep would she be able to shear in 25 days?
Who sheared sheep at a faster daily rate? Sean or Jenny?
Movie World theme park on the Gold Coast had 2325 visitors enter over the course of 7.5 hours on Wednesday. On Friday, it had 2050 visitors enter over a 5 hour period.
If there are more than 380 people entering the park per hour, then Movie World adds extra staff at the gate.
State the rate at which visitors were entering the park per hour on Wednesday.
State the rate at which visitors were entering the park per hour on Friday.
On which day were extra staff required?
A Wisconsin freight train travels 50 \text{ km/h} faster than the intercity passenger train. The Wisconsin freight train travels 600 \text{ km} in the same time that it takes the intercity passenger train to travel only 400 \text{ km}.
Express v, the speed of the Wisconsin freight train in terms of s, the speed of the intercity passenger train.
Express the travel time of the intercity passenger train in terms of s.
Express the travel time T of the Wisconsin freight train in terms of s.
Using parts (b) and (c), form an equation and hence determine the speed of the intercity passenger train.
Hence find v, the speed of the Wisconsin freight train.
Lachlan cycles at v \text{ km/hr} to San Diego while Ryan cycles at s \text{ km/hr} to Los Angeles in the same amount of time. Lachlan covers 48 \text{ km}, while Ryan covers 68 \text{ km}. Lachlan travels at a speed that is 5 \text{ km/h} slower than Ryan.
Express Lachlan's speed v in terms of Ryan's speed, s.
Write down an expression for the number of hours Ryan took to cover his distance, in terms of s.
Write down an expression for the number of hours Lachlan took to cover his distance, in terms of s.
Using parts (b) and (c), form an equation and hence find Ryan's speed
Hence find v, the speed at which Lachlan cycles.
Neville is deciding between 4 cars to buy. He wants to buy the most fuel efficient one.
Complete the table.
| \text{Car} | \text{Litres used} | \text{Distance travelled (km)} | \text{L/km} |
|---|---|---|---|
| \text{Magnum} | 13.405 | 38.3 | |
| \text{Falcador} | 20.71 | 54.5 | |
| \text{Canyonero} | 6.336 | 19.2 | |
| \text{Civil} | 2.754 | 8.1 |
Which car is the most fuel efficient?
Fuel consumption is usually given in \text{L/} 100 \text{ km}. Calculate the fuel consumption rate for the Magnum to this rate.
A car travels 80 \text{ km} and consumes 6.96 \text{ L} of fuel.
Find the rate of fuel consumption of the car in \text{ L/km}. Round your answer to three decimal places.
State the rate of fuel consumption of the car in \text{L/} 100 \text{ km}.
Find the rate of fuel consumption for each car in \text{L/} 100 \text{ km}:
A car travels 50 \text{ km} and consumes 7 \text{ L} of fuel.
Fiona's car can travel 12\,500 \text{ km} on 504 \text{ L} of fuel.
Tom's car can travel 5000 \text{ km} on 1260 \text{ L} of fuel. Susana's car can travel 1600 \text{ km} on 192 \text{ L} of fuel.
Find the rate of fuel consumption of:
Tom's car in \text{L/} 100 \text{ km}
Susana's car in \text{L/} 100 \text{ km}
Who has the most fuel efficient car?
Christa and Ben each own a car, but they decide to carpool together to save money. They want to figure out whose car will be cheaper to run.
Christa's car has a rate of fuel consumption of 5 \text{ L/} 100 \text{ km}. Ben's car has a fuel economy of 35 \text{ km/L}.
Calculate the fuel economy of Christa's car in \text{km/L}. Round your answer to the nearest whole number.
Whose car should they take to save fuel?
John and Tracy each own a car, but they decide to carpool together to save money. They want to figure out whose car will be cheaper to run.
John's car has a rate of fuel consumption of 5.8 \text{ L/} 100 \text{ km}. Tracy's car has a fuel economy of 16 \text{ km/L}.
Calculate the fuel economy of John's car in \text{km/L}, to two decimal places.
Whose car should they take to save fuel?
Determine whether each girl's car is more efficient or less efficient than the reported car fuel consumption:
A make of car is reported to have a rate of fuel consumption of 6.6 \text{ L/}100 \text{ km}. Sharon has this make of car and has calculated the rate of her fuel consumption to be 0.186 \text{ L/km}.
A make of car is reported to have a rate of fuel consumption of 7.1 \text{ L/} 100 \text{ km}. Skye has this make of car and has calculated the rate of her fuel consumption to be 0.041 \text{ L/km}.