Q&A - PSLE Math

[lizawa]

[quote]Hi


Need a help on the question below. Wondering if any one can help? Its a foundational math qn, it seem hard. Thanks!

Question
A restaurant had the same number of apples, oranges and pears at first. After 38 pears, some apples and oranges were used, there were 90 fruits left. There are twice as many apples as oranges left.
The number of pears left were 15 fewer than the number of apples left.

(a) How many pears were left?
(b) How many apples, oranges and pears were there altogether at first?[/quote]At first
A : O : P
1 : 1 : 1

After
2p : 1p : 1u -38

90 fruits left, so
3p + 1u -38 = 90
3p + 1u = 128
1u = 128 - 3p


Pears were 15 fewer than apples

2p - 15 = 1u - 38
1u = 2p + 23

Solve the 2 equations
1p = 21
1u = 65

a) pears left -> 65 - 38 = 27
b) at first -> 3u = 195

[jarenchuatw]

Help needed for these 2 questions - many thanks in advance!


1. Mr Rani and Mr Chau drove along the same route from City X to City Y. Ms Rani took 12 hours while Mr Chua took 9 hours to complete the whole journey. Their difference in their average sped was 15 km/hr.
a) What was the distance between the 2 towns?
b) What was the average speed of Mr Chua?

2. A block of wood 40cm by 14cm by 8 cm was cut into smaller pieces which were 7cm by 6cm by 2cm each. What was the maximum number of pieces that it could be cut into?

[lizawa]

[quote]Help needed for these 2 questions - many thanks in advance!


1. Mr Rani and Mr Chau drove along the same route from City X to City Y. Ms Rani took 12 hours while Mr Chua took 9 hours to complete the whole journey. Their difference in their average sped was 15 km/hr.
a) What was the distance between the 2 towns?
b) What was the average speed of Mr Chua?[/quote]Common distance question. Use ratio of speed and time to solve
TR : TC
12 : 9
SR : SC
9 : 12

3u -> 15
1u -> 5
speed of Rani -> 5 * 9 = 45 km/h
Distance = 45 * 12 = 540 km

Speed of chua -> 12 * 5 = 60km/h

[lizawa]

[quote]Help needed for these 2 questions - many thanks in advance!

2. A block of wood 40cm by 14cm by 8 cm was cut into smaller pieces which were 7cm by 6cm by 2cm each. What was the maximum number of pieces that it could be cut into?[/quote]Need to maximize each side of the wood.

Place 7cm on the 14cm side. 2cm on the 8cm side. 6cm on the 40 cm side.

You get 2 *4 * 6 = 48

[MathIzzzFun]

Easy-going:

Beaker A and Beaker B contain some water. If 46.5ml of water is drained from Beaker A, the volume of the water in beaker A will be 60% that of the water in Beaker B.

If 35.2 ml of water is drained out from Beaker B, the volume of the water in Beaker B will be 85% that of the water in Beaker A.
What is the tota volume of water in Beaker and Beaker B?

hi

at first,
(add 46.5 ml back to Beaker A) Beaker A : Beaker B --> 3u + 46.5 : 5u

If 35.2ml drained from Beaker B,
Beaker A : Beaker B
--> 3u + 46.5 : 5u - 35.2 = 100 : 85 = 20 : 17

equalize/cross-multiply:
51u + 790.5 = 100u - 704
1u --> 30.5
Volume of water in
Beaker A --> 3 x 30.5 + 46.5 = 138 ml
Beaker B --> 5 x 30.5 = 152.5 ml

Total, Beaker A + Beaker B --> 290.5m

cheers.

[nounou]

Dear Tianzhu, HELP please! :?:


:? I don't understand \"Hence, 1 unit of bookmark ------- 12/6 ------- 2
1 unit of bookmarks ------- 8
There is an extra of 6 (8-2) because the bookmark costs 30 cents more than a sticker.
Number of bookmarks ------- 600/30 ------ 20
Therefore cost of 1 bookmark -------- 800/20 ------- 40 cents.\"

Can you please explain? :thankyou: :salute: :udaman:

tianzhu:

anneshirleygilbert:

Can somebody please help with this question?

Betina spent $20 on some stickers and bookmarks. She bought 6 times as many stickers as bookmarks. Each bookmark cost 30 cents more than a sticker. She spent $4 more on the stickers than on the bookmarks. What was the cost of a bookmark?

TIA.

Hi

Amount spent on stickers ------ 12
Amount spent on bookmarks ------- 8

She bought 6 times as many stickers as bookmarks.

Bookmarks ------ 1 unit
Stickers ------- 6 units

Hence, 1 unit of bookmark ------- 12/6 ------- 2

1 unit of bookmarks ------- 8

There is an extra of 6 (8-2) because the bookmark costs 30 cents more than a sticker.

Number of bookmarks ------- 600/30 ------ 20

Therefore cost of 1 bookmark -------- 800/20 ------- 40 cents.

Check

120*10 ------- 1200
20*40 ------ 800

Best wishes

[tianzhu]

Treelodge:

Dear Tianzhu, HELP please! :?:


:? I don't understand \"Hence, 1 unit of bookmark ------- 12/6 ------- 2
1 unit of bookmarks ------- 8
There is an extra of 6 (8-2) because the bookmark costs 30 cents more than a sticker.
Number of bookmarks ------- 600/30 ------ 20
Therefore cost of 1 bookmark -------- 800/20 ------- 40 cents.\"

Hi

I am sorry for the error.

It should be read as 1 unit of stickers instead of bookmarks.

I'll revise the original post.

Please draw out the MD as it gives a clearer picture.

Best wishes

[tianzhu]

jarenchuatw:

2. A block of wood 40cm by 14cm by 8 cm was cut into smaller pieces which were 7cm by 6cm by 2cm each. What was the maximum number of pieces that it could be cut into?

Hi

One way of looking at this question.

Hope this helps.

Best wishes

http://farm9.staticflickr.com/8001/7485835564_8dc81c8d0e_z.jpg\">

[mistychances]

Hi, saw this worked example in My Pals are Here.


Do not understand why the ''crooked'' path is being calculated as a straight path. Isn't a crooked one longer than a straigth one?

Will appreciate if someone can help to explain to me. Thank You

http://i47.tinypic.com/4jipk.jpg\">

[jarenchuatw]

Thanks BB, but could u explain how did u derive the below equation

SR:SC
9:12

How did u derive this equation?

Common distance question. Use ratio of speed and time to solve
TR : TC
12 : 9
SR : SC
9 : 12

3u -> 15
1u -> 5
speed of Rani -> 5 * 9 = 45 km/h
Distance = 45 * 12 = 540 km

Speed of chua -> 12 * 5 = 60km/h