Gillian and Cadence packed 4000 presents for an orphanage. The time Gillian took to pack 7 presents was similar to the time Cadence took to pack 9 presents. They earned 45₵ for every present packed. An additional $1.50 was earned for every 30 presents packed. How much more did Cadence earn than Gillian?
4000 ÷ (7 + 9) = 250
250 × 7 = 1750
250 × 9 = 2250
1750 × 45₵ = $787.50
1750 ÷ 30 = 58 R 10
$787.50 + 58 × $1.50 = $874.50
2250 × 45₵ = $1012.50
2250 ÷ 30 = 75
$1012.50 + 75 × $1.50 = $1125
$1125 − $874.50 = $250.50
Maurice had some $5-notes and twice as many $2-notes.
The total value of all her notes is $207.
Find the value of all her $2-notes.
2 × $2 = $4
$5 + $4 = $9 per group
$207 ÷ $9 = 23 groups
23 × 2 = 46 (Number of $2 notes)
46 × $2 = $92
A container measuring 1.2 m by 65 cm by 40 cm was filled with water. At 3.30 p.m., water from a tap was turned on to fill the container at a rate of 3.25 l per minute. When the container was filled, the base of the container cracked and water leaked out of the container at a rate of 1250 ml per minute.
|(a)||How many litres of water were there in the tank at first?|
|(b)||At what time will the tank be completely filled?|
Shawn, Collin and Eddie bought some marbles to play against each other.
In the first round, Shawn lost half of his marbles to Eddie.
In the second round, Collin won some marbles from Eddie and his number of marbles doubled.
How our students benefit from Just Mathematics?
– Holistic and Accelerated Approach to Learning Math Concepts
– Specially Designed In-house Curriculum Framework
– Ample Practices with Comprehensive Worked Examples
Appreciation of Maths
Through our special sections:
– History of Maths
– Investigative Maths
Customised curriculum to meet the needs of IP students
Exam-Oriented (School/’O’-Level Based) Revision Papers
– To provide intensive practice
– And for tutors to assess students’ understanding before their examinations
A contractor agrees to lay a road of length 3000 m in 20 days. He employs 80 men who work 8 hours a day. After 15 working days, he finds that only 2000 m of the road is completed. How many more men should he employ so as to finish the work on time if each man now works 10 hours a day?
|No. of hours worked in 15 days||= 8 × 15
|Remaining no. of hours to work||= 5 × 10
|Remaining length of road to lay||= 2000 – 1000
= 1000 m
Let the number of workers be x and the total number of hours be y.
Since the number of workers is inversely proportional to the total number of hours,
Let the number of workers be x and the total length of road be l.
Since the number of workers is directly proportional to the length of road,
Therefore, 96 – 80 = 16 more men are required.
In a bridge structure, the mast above each pillar is 87 metres high. The gradient at which the longest steel cable is connected to the centre of the bridge is such that the ratio of vertical distance : horizontal distance is 29 : 57.
a) Show that the angle, α , is 63.03° correct to 2 decimal places.
b) Calculate the length of 2 pieces of the longest steel cable attached from the top of the mast to the centre of the bridge.
Crime Scene Investigation
A dead body was discovered in Hotel California, Room 104 at 10.00 a.m. The pathologist measured the temperature of the body to be 34°C and the room temperature at that instant is 20°C.
What is the time of death?