Tang:

tianzhu:

[quote=\"Drdj\"][Moderator's note: Topics merged.]


This is from Nanyang SA1 2008.
Could someone help me to solve this sum without guess-and-check method? (this was the worked solution)

Wayne has five more 50 cent coins than 20 cent coins. After he used eight 50 cent coins, the value of 50 cent conis is $1.50 more than the value of 20 cent coins. How many coins did he have at first?

Thanks in advance.

This question is from Nanyang P6 SA1 2008.
http://wendykoh.com/08/primary6-nanyangsa1-maths.pdf

We need Chiefkiasu's help to move it to the right thread.

[/quote]8 - 5 = 3. [Remove 5, so number of 50-cent and 20-cent coins supposed to be the same. But since he spent 8 50-cent coins, he now has 3 50-cent coins less.]
3 50¢ = 150¢.
150 + 150 = 300 ¢ (more). [Putting back the 3 50-cent coins, the amount of 50-cent coins will be 300 cents more than the amount of 20-cent coins.]
50 - 20 = 30¢ (more) [The difference between 1 50-cent coin and 1 20-cent coin]
300 ÷ 30 = 10 20¢ coins. [Total difference / One difference gives you the number of 20-cent coins. To get the number of 50-cent coins, you will need to 5.]

To solve such problem sum, always try to make the number of coins the same.

Dharma:

fxchow:

hi tianzhu,


Wish you have a nice weekend too!

BTW, do you have any tips to handle P6 math? i really lost.

In fact, my girl likes math and scored good results in P4 & P5.
But this year I can see that she is facing difficulty.
She confuses with the ratio, fraction & percentage....now add on speed, circle.....

Perhaps someone can recommend a \"specialist\" math tutor or tuition center in West to me. TIA

Dear fxchow,

I understand your worry for your child but if she has handled her P4 and P5 work well she will have a strong foundation already. Ratio, fraction and percentage are P5 topics and are carried forward to P6 but at a higher level. Only new topics in P6 are speed and circles.

Regarding ratio, fraction and percentage....they are all related and are the same things expressed differently.

I notice most parents produce beautiful solutions to problems sums using the model method. For some reason or another, I prefer the units method as I find it a faster method.

If you notice most problem sums under fractions and percentages can be expressed in ratio form.

You child needs to be able to quickly express percentages in form of fractions. Once you know the fraction, express it in ratio to solve the problem. Ratios are very useful and will help your child ..... when we draw models to express fractions or percentages, we are expressing the ratio of two or more objects in a pictorial form.

Once you it is in ratio form...get her to read the question carefully and move on. The questions asked are normally very standard....

Important to get the basics right ...

For speed, 2 main type of qns ...meeting and catching up. Your child need to be able to handle these 2 types. Go thru school worksheets/textbook for the process.

Ratio is important when comes to speed qns.

Need to understand,
1.For a fixed distance, the ratio of the speed of 2 vehicles will be inversely proportional to ratio of the time taken by the 2 vehicles.

2. For a fixed time, ratio of speed of 2 vehicles is same as the ratio of the distance travelled by the 2 vehicles.

For circles, must know area and perimeter of circle. But problem is normally ...the diagram given is more complicated than a simple circle. Your child need to have clear mind on how to manipulate/shift/slide the figures/diagram....she needs good sleep before the exam to do this.

As regards to Maths tuition...you may wish to try Maths Hub at Bukit Batok ..my older daughter went there for her SMOP training 2~3 years ago. They also do PSLE maths and have different classes for different learning abilities.

Just get you child to understand how fractions and percentages are expressed in ratios ....guess things will not be so confusing anymore.

Fractions and Percentages can be converted to Whole Numbers.

Eg 1) A is 4/5 of B.
A -- 4 units
B -- 5 units

2) A is 40% of B
A -- 4 units
B -- 10 units
or simplify further into
A -- 2 units
B -- 5 units

3) Total number of apples and oranges is 100. After 2/3 of apples and 1/4 oranges are removed, the number apples and apples left is 40. [Numbers may not make sense]

3 Au + 4 Ou = 100
1 Au + 3 Ou = 40
Then solve.
Just remember that total number of apples is 3 Au and total number of oranges is 4 Ou.

Good Luck!

Vanilla Cake:

4). Mr Andrew started his journey from Singapore to KL. After completing 2/9 of the \tjourney, he overtook a bus, which was travelling at a uniform speed of 80km/h in the same direction. When Mr Andrew reached KL 3 hours after overtaking the bus, the bus still had another 82km to travel before reaching KL. If Mr Andrew travelled at an average speed of 90km/h, how long did he take to arrive at KL? Give your answer in hours and minutes.

A4.
7/9 of the journey-> 80x3 + 82 = 322 km
Total distance -> 322/7x9 = 414 km
Time taken => 414/90 = 4 & 3/5 h = 4 h 36 min

Time taken for Mr Andrew to arrive at KL was 4 h 36 min

I tried working backwards and find it strange.
7/9 of the journey (bus)-> (80x 3) +82 = 322 km
7/9 of the journey (car) -> 90x 3 = 270 km
By right, both figures should be the same.Where did you get this question from? :?

3 h -- 82 km
1 h -- 82 / 3 = 27 1/3 km/h

Speed of Car = 80 + 27 1/3 = 107 1/3 km/h

7/9 D = 107 1/3 x 3 = 322 km

D = 9/7 x 322

Time at 90 km/h = 9/7 x 322 / 90 = 4.6 h = 4 h 36 min

Vanilla Cake:

1). Tap A took 3 minutes to fill up a tank. Tap B took 4 minutes to fill up the same tank. However, if you pulled out the plug at the bottom of the tank, the tank could empty in 12minutes. If both the taps are turned on and the plug pulled out at the same time, how long would it take for the tank to be filled up?


2). Denise & Jeanette went shopping with a total of $380. After buying same items each, the amount Denise has left is 4 times the amount she spent and the amount Jeanette has left is thrice the amount she spent. The 2 girls had a total of $296 left. How much did Denise have at first?

4). There were 720 apples and oranges in a big carton.
1/6 of the apples and 1/3 of the oranges were from China.
The rest were from Australia.
If a total of 170 apples and oranges were from China,
(a). How many apples were in the big carton?
(b). How many oranges were from Australia?

5). Jane had 4 times as much money as Grace. After their mother gave Jane $62.10 and Grace $25, Jane had 3 times as much money as Grace. How much money did Jane have at first?

6). From Jan to Feb, a salesman’s monthly income increased by 20%. However, from Feb to Mar, it decreased by 25%.
If his income in Mar was $450 less than his income in Jan, what was his income in Feb?

7). Rafi receives $2 from his mother for every $10 he saves. He also received $3 from his father for every $20 he saves. He has $174 altogether after some times.
(a). How much of money is from his mother?
(b). How much of it is from his father?

1). Tap A took 3 minutes to fill up a tank. Tap B took 4 minutes to fill up the same tank. However, if you pulled out the plug at the bottom of the tank, the tank could empty in 12minutes. If both the taps are turned on and the plug pulled out at the same time, how long would it take for the tank to be filled up?

A: 3 min - 1 tank
1 min - 1/3 tank

B: 4 min - 1 tank
1 min - 1/4 tank

E: 12 min - 1 tank
1 min - 1/12 tank

A + B - E: 1 min -- 1/3 + 1/4 - 1/12
= 6/12 = 1/2 tank
1/2 tank -- 1 min
1 tank -- 2 min

2). Denise & Jeanette went shopping with a total of $380. After buying same items each, the amount Denise has left is 4 times the amount she spent and the amount Jeanette has left is thrice the amount she spent. The 2 girls had a total of $296 left. How much did Denise have at first?

5 Du + 4 Ju -- $ 380 ==> 15 Du + 12 Ju -- 1140
4 Du + 3 Ju -- $296 ==> 16 Du + 12 Ju -- 1184

1 Du -- 1184 - 1140 = 44
5 Du -- 5 x 44 = $220


4). There were 720 apples and oranges in a big carton.
1/6 of the apples and 1/3 of the oranges were from China.
The rest were from Australia.
If a total of 170 apples and oranges were from China,
(a). How many apples were in the big carton?
(b). How many oranges were from Australia?

6 Au + 3 Ou = 720
1Au + 1 Ou = 170 ==> 3 Au + 3 Ou = 510

3 Au = 720 - 510
1 Au = 210 / 3 = 70
a) A: 6 Au = 6 x 70 = 420 apples in the big carton.

1 Ou = 170 - 70 = 100
b) 2 Ou = 2 x 100 = 200 oranges from Australia


5). Jane had 4 times as much money as Grace. After their mother gave Jane $62.10 and Grace $25, Jane had 3 times as much money as Grace. How much money did Jane have at first?

J - 4 Units
G - 1 Unit

JN -- 4 Units + $62.10 = 3 Parts
GN -- 1 Unit + $25 = 1 Part ==> 3 Units + $75 = 3 Parts

4 Units + 62.10 = 3 Units + 75
1 Unit = 75.00 - 62.10 = 12.90

J: 4 Units = 4 x 12.90 = $51.60


7). Rafi receives $2 from his mother for every $10 he saves. He also received $3 from his father for every $20 he saves. He has $174 altogether after some times.
(a). How much of money is from his mother?
(b). How much of it is from his father?


1 set (Saving $20 + Father $3 + Mother 2 x $2) -- 20 + 3 + 2 x 2 = 27
174 / 27 = 6 r 12
6 sets -- 6 x 2 x $2 = $24
remainder 12 -- $2
a) Mother -- 24 + 2 = $26

b) Father -- 6 x 3 = $18

faith2u:

[Moderator's note: Topics merged.]


Ai Tong (CA1 – 2004)
3). At train has a number of passenger when it left Terminal A.
At station B, 2/5 of them got off and 80 passengers got on.
At station C, 223 passengers got off and 38 got on.
The train than had 3/8 of the number of passengers when it left station B.
(a). How many passengers were in the train when it left station C?
(b). How many passengers were in the train when it left Terminal A?

A -- 5 Units
B -- 3 Units + 80 = 8 Parts
C -- 3 Parts = 3 Units + 80 - 223 + 38 = 3 Units -105

5 Parts -- 223 - 38 = 185
1 Part -- 185 / 5 = 37
a) C:3 Parts -- 3 x 37 = 111 passengers

8 Parts --> 8 x 37 = 296
3 Units -- 296 - 80 = 216
b) A: 5 Units -- 5/3 x 216 = 360 passengers

tianzhu:

Thank you for your help.


RGPS SA1 2008
http://farm4.static.flickr.com/3639/3465444648_9b5f70ab2f_o.jpg\">

Draw a bar and divide it into 10 days.
Draw another bar of same size and divide it into 18 days.

From the two bars, you will notice that the number of days meet at midpoint and 5 + 9 = 14 days.

So Jane took 5 days.

1. David had 2 bags of marbles. After he had sold 44 marbles from Bag X to his friend, the number of marbles in Bag Y was 5/7 of the number of marbles in Bag X. Given that there were 2/5 as many marbles in Bag Y as in Bag X originally, find the number of marbles in Bag X at first.


5 Y = 2 X ==> 35 Y = 14 X

7 Y = 5 (X - 44) ==> 35 Y = 25 (X - 44)

25 (X - 44) = 14 X
11 X = 25 x 44
X - 25 x 44 / 11 = 100 marbles at first.


2. John read a book in 3 days. He read 35% of the total number of pages in the book on the 2nd day. The ratio of the total number of pages of book he read on the 1st and 2nd day to the number of pages he read on the 3rd day was 11:9. If he had read 75 more pages on the 3rd day than on the 1st day, how many pages of the book did he read on the 2nd day ?

2nd day –> 35%
1st + 3rd days –> 65%
3rd day –> 9/20 x 100% = 45%
1st day –> 65% - 45% = 20%

25% –> 75 pages
2nd day: 35% –> 35/25 x 75 = 105 pages.