Q&A - P5 Math

[KP2]

Hi , need help with this one - preferably in bags & boxes method


There were some 50-cent coins and twice as many 20-cent coins in a box. Melissa added forty 50-cent coins and eight 20-cent coins into the box. As a result, there were 4 times as much amount of money as before.

(a) What was the total number of coins in the box at first?
(b) What was the total value of all 20-cent coins in the box in the end?

[Maths Hub]

KP2:

Hi , need help with this one - preferably in bags & boxes method


There were some 50-cent coins and twice as many 20-cent coins in a box. Melissa added forty 50-cent coins and eight 20-cent coins into the box. As a result, there were 4 times as much amount of money as before.

(a) What was the total number of coins in the box at first?
(b) What was the total value of all 20-cent coins in the box in the end?

Hi KP2,

a)\tSince Melissa added forty 50-cent coins and eight 20-cent coins into the box,
a total of 40 × 0.50 + 8 × 0.20 = $21.60 is added.

Amount of money at start\t:\tAmount of money in the end
1\t\t\t :\t\t4

3 Units --> $21.60
1 Unit --> $21.60 ÷ 3 = $7.20

So the amount of money at the start is $7.20

Since the number of 20-cent coins is twice that of 50-cent coins at the start, we use grouping method to obtain the number of coins. Each group will contain three coins: two 20-cent coins and one 50-cent coin. The value of each group is $0.90.

Total groups --> $7.20 ÷ $0.90 = 8
Total number of coins at the start --> 8 × 3 = 24

b)\tNumber of 20-cent coins at the start --> 8 × 2 = 16
Number of 20-cent coins in the end --> 16 + 8 = 24
Value of all the 20-cent coins in the box in the end --> 24 × 0.20 = $4.80

Check:
Start:
20-cent coins --> 16
50-cent coins --> 8
Total Value --> 16 × 0.20 + 8 × 0.50 = $7.20
End:
20-cent coins --> 24
50-cent coins --> 8 + 40 = 48
Total Value --> 24 × 0.20 + 48 × 0.50 = $28.80 (CORRECT since it is 4 times the original value of money in the bag)

[wahwah]

Hi,

Need help with this question. Many thanks in advance!

There are two bags of stones labelled A and B. In Bag A, the are 26 black stones and 20 white stones. In Bag B, there are 39 black stones and 30 white stones. How many black and white stones should be transferred from Bag B to Bag A such that 60 % of the stones in Bag A and 50% of those in Bag B are black?

[Maths Hub]

wahwah:

Hi,

Need help with this question. Many thanks in advance!

There are two bags of stones labelled A and B. In Bag A, the are 26 black stones and 20 white stones. In Bag B, there are 39 black stones and 30 white stones. How many black and white stones should be transferred from Bag B to Bag A such that 60 % of the stones in Bag A and 50% of those in Bag B are black?

http://i45.tinypic.com/29vf382.jpg\">

[wahwah]

Hi Maths Hub,

Thanks so much for the prompt solution!

[Dad8282]

Hi, need help to answer the following questions from NanHua 2011 SA2 Paper 2.


Q1. A quarter of Jovern’s mass is twice that of Evelyn’s mass. Find the ratio of Eveyln’s mass to Jovern’s mass.

Q6. 36 scouts were told to line up in a row along one side of the square-shaped Assembly Ground from corner to corner at an equal spacing of 1.2m apart to play a game.
Just before the game, 7 of them had to leave and help their teacher with some chores. As a result, the remaining scouts had to line up along the same side of the Assembly Ground at a new equal spacing.
What was the new spacing between 2 scouts?

Q13. Hannah collected $6720 from the sale of some dresses and blouses. The ratio of the price of a dress to the price of a blouse is 5:1. Each blouse costs $5. Even the total number of blouses sold made up 20% of the total number of dresses and blouses sold, how many dresses were sold by Hannah?

Q15. The figure below shows Tap A, Tap B and an empty tank with a capacity of 96.8 litres. Water flows from Tap A at 6.4 litres per minute and Tap B 5.6 litres per minute.
Tap A was turned on first. Tap B was turned on 2 minutes later. The taps were turned off at the same time when the tank was completely full without overflowing.
How much water flowed from Tap B?

My DD answer:
Tap A, 2 mins – 6.4l X 2 = 12.8l
Both taps, 3 mins – 12.8l + 6.4l + 5.6l = 24.8l
At 4 mins – 24.8l + 12l = 36.8l
At 5 mins – 36.8l + 12l = 48.8l
At 7 mins – 48.8l + (12l X2) = 72.8l
At 9 mins – 72.8l + 24l = 96.8l

Tap B – (9 mins – 2 mins) X 5.6l = 39.2l

Is there a shorter way to answer this Q?

Thanks!

[Maths Hub]

Dad8282:

Hi, need help to answer the following questions from NanHua 2011 SA2 Paper 2.


Q1. A quarter of Jovern’s mass is twice that of Evelyn’s mass. Find the ratio of Eveyln’s mass to Jovern’s mass.

Q6. 36 scouts were told to line up in a row along one side of the square-shaped Assembly Ground from corner to corner at an equal spacing of 1.2m apart to play a game.
Just before the game, 7 of them had to leave and help their teacher with some chores. As a result, the remaining scouts had to line up along the same side of the Assembly Ground at a new equal spacing.
What was the new spacing between 2 scouts?

Q13. Hannah collected $6720 from the sale of some dresses and blouses. The ratio of the price of a dress to the price of a blouse is 5:1. Each blouse costs $5. Even the total number of blouses sold made up 20% of the total number of dresses and blouses sold, how many dresses were sold by Hannah?

Q15. The figure below shows Tap A, Tap B and an empty tank with a capacity of 96.8 litres. Water flows from Tap A at 6.4 litres per minute and Tap B 5.6 litres per minute.
Tap A was turned on first. Tap B was turned on 2 minutes later. The taps were turned off at the same time when the tank was completely full without overflowing.
How much water flowed from Tap B?

My DD answer:
Tap A, 2 mins – 6.4l X 2 = 12.8l
Both taps, 3 mins – 12.8l + 6.4l + 5.6l = 24.8l
At 4 mins – 24.8l + 12l = 36.8l
At 5 mins – 36.8l + 12l = 48.8l
At 7 mins – 48.8l + (12l X2) = 72.8l
At 9 mins – 72.8l + 24l = 96.8l

Tap B – (9 mins – 2 mins) X 5.6l = 39.2l

Is there a shorter way to answer this Q?

Thanks!

Q1. A quarter of Jovern’s mass is twice that of Evelyn’s mass. Find the ratio of Eveyln’s mass to Jovern’s mass.

Since a quarter of Jovern’s mass is twice that of Evelyn’s, an eighth of Jovern mass is same as that of Evelyn’s. Therefore ratio = 1 : 8

Q6. 36 scouts were told to line up in a row along one side of the square-shaped Assembly Ground from corner to corner at an equal spacing of 1.2m apart to play a game.
Just before the game, 7 of them had to leave and help their teacher with some chores. As a result, the remaining scouts had to line up along the same side of the Assembly Ground at a new equal spacing.
What was the new spacing between 2 scouts?

Number of Spaces between 36 scouts --> 35 spaces
Length of the line --> 35 × 1.2 = 42 m
Number of Spaces between 29 scouts --> 28 spaces
New Spacing --> 42 ÷ 28 = 1.5 m

Q13. Hannah collected $6720 from the sale of some dresses and blouses. The ratio of the price of a dress to the price of a blouse is 5:1. Each blouse costs $5. Even the total number of blouses sold made up 20% of the total number of dresses and blouses sold, how many dresses were sold by Hannah?

Price of Blouse --> $5
Price of Dress --> $25
Since the total number of blouses sold made up 20% of the total number, the ratio of blouses sold: dresses sold = 1 : 4
We use grouping method to solve this, with each group having 4 dresses and 1 blouse. The cost of each group is 5 + 4 × 25 = $105
Number of groups --> 6720 ÷ 105 = 64
Number of dresses sold --> 64 × 4 = 256

Q15. The figure below shows Tap A, Tap B and an empty tank with a capacity of 96.8 litres. Water flows from Tap A at 6.4 litres per minute and Tap B 5.6 litres per minute.
Tap A was turned on first. Tap B was turned on 2 minutes later. The taps were turned off at the same time when the tank was completely full without overflowing.
How much water flowed from Tap B?

After 2 min, 96.8 – 6.4× 2 = 84 litres left.
After the 2 min, every min, both A and B will fill the tank at a combined rate of 5.6 + 6.4 = 12 litres.
Number of min both taps are on to fill up the 84 litres --> 84 ÷ 12 = 7 min
Therefore, A was on for 9 min and B was on for 7 min.
Amount of water flowed from tap B --> 7 × 5.6 = 39.2 litres

[Dad8282]

Hi Maths Hub,


:thankyou: for the fast response!

[KP2]

Hi Maths hub ,

Thank you for your help

[KP2]

Hi Maths hub ,

Thank you for your help