Q&A - PSLE Math

[pandu]

20% of the people in a school hall are teachers and the rest are pupils. 75% of the pupils are boys and there are 72 more boys than girls. How many boys must leave the hall so that 20% of the people in the hall are boys?

[corneyAmber]

pandu:

Emily earns a commission on 12% for the first 5 encyclopaedias she sells. For any additional sales, she will get a 15% commission.

Each encyclopaedia is sold at $140. If she receives a total commission of $462, how many encyclopaedias does she sell altogether?

5x140 = 700
0.12 x 700 = $84
462 - 84 = 378 (commission made from additional sales)

Let u be the number of units sold after 5 units were sold.
0.15*u*140 -> 378
21u -> 378
u-> 18

Total encyclopaedias sold = 18+5 = 23

[small]

cimman:

small:

Hi,


Please help and many thanks in advance.

http://i49.tinypic.com/331lstd.jpg\">

http://i48.tinypic.com/24o5c85.png\"> http://i47.tinypic.com/14lls41.png\">

as you can see from the above tessellations, there are quite a few options for the larger shape. I've highlighted one of the options in red outline for each tessellation.

Thanks a lot Cimman..

[corneyAmber]

pandu:

20% of the people in a school hall are teachers and the rest are pupils. 75% of the pupils are boys and there are 72 more boys than girls. How many boys must leave the hall so that 20% of the people in the hall are boys?

u-u-u-u (3u=boys, because 75% of pupils, u = girls)
u (u = teachers)

3u = u+72
u = 72/2 = 36
Total people = 5u= 180
Total boys =3u = 108
Let b be the boys that left the hall.
(108-b)/(180-b) = 1/5 (20% of people are boys after b boys left)
5(108-b) = 180-b
540 - 5b = 180 -b
4b = 360
b =90
So 90 boys must leave to have 20% of people in the hall as boys.

[Check: 108-90=18, 180-90 = 90 and 18/90 = 1/5 = 20%]

[its888me]

Thanks tianzhu of giving great tips on the eye problem!

[its888me]

its888me:

So sorry, another question from Nanyang prelim 2010 again, Q11:


Diagram A shows a closed rectangular tank of dimensions 20cm by 20cm by 40cm with a cube of edge 10cm glued to its bottom left corner. The tank contains 12 litres of water.

Diagram B shows the same rectangular tank lying on its side. Find the height of the water level, in cm, corrected to 2 decimal places.

http://i48.tinypic.com/302o09z.jpg\">

Again, TIA!

Can someone help with this question? My child assumed that in the Diagram B, the water level reached at the 1/2 point at the cube, thus, getting the answer 14.36cm. Given answer is 15.71.

Again, thanks a lot!

[speedmaths.012624com]

its888me:

its888me:

So sorry, another question from Nanyang prelim 2010 again, Q11:


Diagram A shows a closed rectangular tank of dimensions 20cm by 20cm by 40cm with a cube of edge 10cm glued to its bottom left corner. The tank contains 12 litres of water.

Diagram B shows the same rectangular tank lying on its side. Find the height of the water level, in cm, corrected to 2 decimal places.

http://i48.tinypic.com/302o09z.jpg\">

Again, TIA!

Can someone help with this question? My child assumed that in the Diagram B, the water level reached at the 1/2 point at the cube, thus, getting the answer 14.36cm. Given answer is 15.71.

Again, thanks a lot!

Hi,

Let's try this method:

First,
find the \"Volume of Air\" at top part of Diagram A.
(Vol of air) = (Vol of tank) - (Vol of water) - (Vol of cube).

Next,
find height (or depth) of air at top of Diagram B.
(Height of air) = (Vol of air) / (nett Base Area)
nett Base Area = (40 x 20) - (10 x 10)

Finally,
Height of water = 20 cm - (height of air)

Can you work from here?

Hope this helps.

Cheers

speedmaths.com


.

[tianzhu]

Essential:

Need help, please kindly assist. At 11am a car left town P for Town Q. Travelling at a speed of 80 km/h. At the same time , another car left town Q for town P at a speed of 100 km / h . The distance between the two towns was 720 km.at what time did the cars pass each other ?

Hi

Good Morning.

As usual for Speed questions, start with a simple diagram.

In 1h, the two cars covered 180 km (100 + 80).

When they pass each other or meet, they cover the entire distance between P and Q which is 720 km.

720/180 ------- 4 h

Hence, they passed each other at 3 pm.

Alternatively, if students are familiar with inverse proportion, they may also use it to calculate the distance travelled by the two cars.

Speed ratio

Car A: Car B ------- 80:100 ------ 4.5

The distance ratio remains the same as 4:5

9 units ------ 720

1 unit ------ 80

Distance covered by car A ------ 4*80 -------- 320 km

Time taken by car A ------- 320/80 -------- 4h

You may also use the distance covered by Car B and get the same answer of 4h.

In this case,(5*80)/100 ------ 4h

Best wishes

[Essential]

Good morning Tianzu, thank u very much for helping …

[Michaelia0816]

Pls help with this questions,


1) In a class, there are 4 more girls than boys. 1/3 of the boys and 7/11 of the girls take pubic buses to school. If 1/2 of the class takes pubic bus to school, how many pupils are there in the class?

My method:
Girls—1u+4
Boys—1u
In the class—2u+4
Half of the class—1u+2

1-1/3=2/3
1-7/11=4/11
(Take pubic bus) 1u+2-----1/3(boys)+7/11(girls)
(Do not take pubic bus) 1u+2-----2/3( boys)+4/11( girls)
Then, I dun know how to continue the next step, so help…

2) Isa had a total of 1464 orange, yellow and purple balloons for sale. The ratio o the orange balloons to the number of yellow balloons was 2:3. After Isa sold 3/4 of the yellow balloons, 1/2 half of the purple balloons and none of the orange balloons, he had 812 balloons left. How many yellow balloons did Isa have at first?

My answer for this is 960, but I do checking, I found out it is wrong so I really really dun know do this question.