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 x $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?|
|(a)|| × 120 cm × 65 cm × 40 cm
= 104 000 cm3 = 104 000 ml = 104 l
|(b)|| － =
× 120 cm × 65 cm × 40 cm = 52 000 cm3
52 000 cm3 ÷ 3250 cm3 = 16 min
3250 cm3 – 1250 cm3 = 2000 cm3
× 120 cm × 65 cm × 40 cm = 156 000 cm3
|156 000 cm3 ÷ 2000 cm3/min = 78 min
78 min + 16 min = 94 min = 1 h 34 min
|1 h 34 min after 3.30 p.m. → 5.04 p.m.|
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.
When Shawn lost of his marbles to Collin,
When Eddie lost (Collin won), Collin’s marbles were halved:
When Shawn lost half of his marbles to Eddie:
|1 unit||→||360 ÷ 3 = 120|
|24 units||→||24 × 120 = 2880|
The three boys had 2880 marbles altogether at first.
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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.
In the diagram, ΔFCE is similar to ΔABE. Given that ΔABC has an area of 24 cm2,
3BC = 2CE and 4DE = DA,
|a)||find the area of ΔACE;|
|b)||find the area of ΔFCE;|
|c)||show that area of ΔCDE = area of ΔABC;|
|d)||find the value of|