Q&A - PSLE Math

[Tang]

suiyuan:

Hi, Mrs Wong


How would you teach your students to solve the following problems?(if feasible by Model Drawing)

1) There are 32 rooms for 71 pupils at a student hostel. At the boys’ side, each room is shared by 2 boys. At the girls’ side, each room is shared by 3 girls. If each room is fully occupied by either 2 boys or by 3 girls, find the number of boys and girls respectively.

2) Alan has 1.5 times as many marbles as Bernard while Carl has 2.5 times as many marbles as Bernard. During a game, both Alan and Carl lost to Bernard and for every 1 marble that Alan lost to Bernard; Carl lost 2 marbles to Bernard. At the end, Alan has 21 marbles left, while Carl has 27 marbles left. How many marbles did Alan lose to Bernard?

3) When Jenny was 40 years old, her son was twice her daughter’s age. Jenny will be twice her son’s age when her daughter is 28 years old. How old will Jenny be when her daughter is 20 years old?

Thank you for your help.

1.
G + B = 71 [x 2]
2G + 2 B = 2 x 71 = 142

G/3 + B/2 = 32 [x 6]
2 G + 3 B = 6 x 32 = 192

B = 192 - 142 = 50 boys

G = 71 - 50 = 21 girls

Or
Suppose all boys, 32 x 2 = 64
71 - 64 = 7 [short fall]
3 - 2 = 1 [Difference in number]
7 / 1 = 7 Rooms for girls

32 - 7 = 25 Rooms for boys

7 x 3 = 21 girls
25 x 2 = 50 boys


2.

A : B : C = 3 : 2 : 5
Change ratio -1 : +3 : -2
AN = 21 and CN = 27

3 Units - Part = 21 [x 2]
6 Units - 2 Parts = 2 x 21 = 42

5 Units - 2 Parts = 27

Unit = 42 - 27 = 15

Part = 3 x 15 - 21 = 24 marbles.


3. Refer to Uncle Observer's Blog - Maths-Whole Number for Model Drawing and answer.

[suiyuan]

suiyuan:

[quote][IMG]http://i697.photobucket.com/albums/vv338/mrsw

Hi Mrs Wong

You may wish to repost the image again.The link doesn't seem to work.
Alternatively, you may click on URL.[/quote]Hi Mrs Wong

I am sorry to inconvenience you again.Could you help to repost the image as that particular link doesn't seem to work.

[Drdj]

Dear all,


Please help me to solve this sum - from CHIJ Prelim 2008
Thanks in advance

http://www.postimage.org/

[AnnT2009]

Please help,


Q1 Mary and Jason each have some money. If Mary spent$80 per day and Jason spent $40 per day. Mary will have $500 left when Jason has spent all his money. If Mary spent $40 per day and Jason spent $80 per day. Mary will have $1100 left when Jason spent all his money. What is the amount of money Jason has?
Ans:$400

Q2 Mr Tan bought three times as many badges as toy cars and spent $144 in total. He spent $84 more on toy cars than on badges. Given that a toy car cost $10.40 more than a badge. What is the cost of a badge?
Ans:$1

TIA.

[tianzhu]

Hi drdj


When you post questions, you don't have to click on quote everytime unless you are referring to it.Otherwise it becomes kind of confusing.

Just click on post reply will do.

[Dharma]

Hi drdj,


Let area large and small shaded sectors be A and B respectively, area of unshaded part of rectangle be C and area of small quarter circle be D

C \t= ((4 X 2) – B)cm2
\t= (8 – B)cm2

A\t = (¼ x 3.14 x 4 x 4 – D – C )cm2
\t\t = (¼ x 3.14 x (42 – 22) – C)cm2
\t\t = (9.42 – (8 – B))cm2
\t\t= (1.42 + B)cm2

Difference between 2 shaded areas, A-B = 1.42cm2

[tianzhu]

Dharma:

Hi drdj,


Let area large and small shaded sectors be A and B respectively, area of unshaded part of rectangle be C and area of small quarter circle be D

C \t= ((4 X 2) – B)cm2
\t= (8 – B)cm2

A\t = (¼ x 3.14 x 4 x 4 – D – C )cm2
\t\t = (¼ x 3.14 x (42 – 22) – C)cm2
\t\t = (9.42 – (8 – B))cm2
\t\t= (1.42 + B)cm2

Difference between 2 shaded areas, A-B = 1.42cm2

Hi Dharma

You may wish to take a look at this again

(¼ x 3.14 x (42 – 22) – C)cm2

Please clarify how you arrive at this.I guess you are referring to the difference in areas between the two quadrants.You must be referring to 4*4 (4square or 4 to the power of 2)

Difference in areas --- (¼ x 3.14 x (4*4 –2*2) – C) sq cm

[Dharma]

Sorry Tianzhu …superscript disappeared when cut and pasted from ms word


Area of larger shaded part(A) = Diff in area of the 2 quadrants - C

A = 1/4 X 3.14 X (4x4 - 2 x2) - C

C = 8 - B

A = 9.42 - 8 + B

So, diff between A & B, i.e. A-B = 1.42

[faith2u]

[Moderator's note: Topics merged.]


1). Father gave Gary $570 and his sister $250. After their mother has
given them an equal amount, Gary’s amount was twice as much as his
sister’s. How much money did their mother give to each of them?
(Ans : $70)

2). 20 more men than women were invited to a concert. ¾ of the men
and 2/3 of the women attended the concert, while 26 people did not
show up.
How many people were invited to the concert? (Ans : 92)

3). An ant is climbing up a slippery wall. After every 3cm it climbs up, it
slides 1cm. It takes 3 seconds for it to climb up 1cm and 1 second for
it to slide 1cm.
(a). How long does it take to climb 12 cm? (Ans : 1min)
(b). How long does it take to climb 60cm? (Ans : 4min 56sec)

[faith2u]

[Moderator's note: Topics merged.]


Question :
Aunty May cooked 520 fishballs and Sotong balls altogether. She sold 75% of the fishballs and 50% of the Sotong balls. She was left with 180 fishballs and Sotong balls altogether. How many fishballs did she cook at first? (Ans : 320)