Q&A - PSLE Math

[S6169]

jieheng:

raghupavithra:

four boys, Alex,Ben,carl and dan shared the cost of a present equally. carl had some money but he did not have enough to pay for his share.Alex paid more to makeup the difference for carl. the amount of money paid by alex is 1/2of the total amount paid by ben, carl and dan. the amount of money paid by ben is 1/3 of the amount paid alex,carl,and dan. the amount of money paid by carl is 1/5 of the total amount paid by alex,ben and dan.if carl returned $38 to alex the next day, find the cost of the present.


how to solve this

the amount of money paid by carl is 1/5 of the total amount paid by alex,ben and dan
Carl paid []
total amount paid by Alex , Ben and Dan [][][][][]

Carl paid 1/6 of the total cost

Carl should pay 1/4 of the total cost as four boys shared the cost of a present equally

the amount that Alex paid more to makeup the difference for carl = 1/4 - 1/6 = 1/12

1u --> 38
12u --> 38*12 = 456

the cost of the present is $456 (Ans)

What is this part for? confuse the student? :roll:

[jieheng]

S6169:

jieheng:

[quote=\"raghupavithra\"]four boys, Alex,Ben,carl and dan shared the cost of a present equally. carl had some money but he did not have enough to pay for his share.Alex paid more to makeup the difference for carl. the amount of money paid by alex is 1/2of the total amount paid by ben, carl and dan. the amount of money paid by ben is 1/3 of the amount paid alex,carl,and dan. the amount of money paid by carl is 1/5 of the total amount paid by alex,ben and dan.if carl returned $38 to alex the next day, find the cost of the present.


how to solve this

the amount of money paid by carl is 1/5 of the total amount paid by alex,ben and dan
Carl paid []
total amount paid by Alex , Ben and Dan [][][][][]

Carl paid 1/6 of the total cost

Carl should pay 1/4 of the total cost as four boys shared the cost of a present equally

the amount that Alex paid more to makeup the difference for carl = 1/4 - 1/6 = 1/12

1u --> 38
12u --> 38*12 = 456

the cost of the present is $456 (Ans)

What is this part for? confuse the student? :roll:[/quote]the amount of money paid by ben is 1/3 of the amount paid alex,carl,and dan
Ben paid []
total amount paid by Alex , Carl and Dan [][][]

==> Ben paid 1/4 of the total cost (which is already mentioned in the question that four boys shared the cost of a present equally and only Carl did not have enough to pay for his share )

the amount of money paid by alex is 1/2of the total amount paid by ben, carl and dan
Alex paid []
total amount paid by Ben , Carl and Dan [][]

==> Alex paid 1/3 of the total cost

the amount that Alex paid extra for Carl = 1/3 - 1/4 = 1/12

which is the same as the amount that Alex paid more to makeup the difference for carl = 1/4 - 1/6 = 1/12

********************************************************

These steps are not require in order to solve this question .

If you do these steps , you will still get the same answer .

[jieheng]

pensiveowl:

Thanks jieheng

Hi pensiveowl ,

You are welcome.

Regards,

[pensiveowl]

I need help with this problem - can someone pls help solve it - thanks


http://www.positivelyquit.org/images/math.jpg\">

[jieheng]

pensiveowl:

I need help with this problem - can someone pls help solve it - thanks

http://i52.tinypic.com/2qxvo1k.jpg\">

Ratio of radius of large semi-circle to radius of medium semi-circle = 8 : 5
==> radius of large semi-circle / radius of medium semi-circle = 8/5
==> radius of large semi-circle = 8/5 * 15 = 24 cm

FG = GH = diameter of medium semi-circle = 2*15 = 30 cm

BC = AD = diameter of large semi-circle = 2*24 = 48 cm

BF = GC = (48-30)/2 = 9 cm

Area of medium semi-circle = 1/2*Pi*15*15 = 225/2*Pi

Area of large semi-circle = 1/2*Pi*24*24 = 288*Pi

Area of un-shaded BEF = Area of un-shaded CHG =Area of square ABFE - area of small quadrant = 9*9 - 1/4 *Pi*9*9 = 81- 81/4*Pi

Area of rectangle EFGH = 9*30 = 270

Area of shaded part
= Area of medium semi-circle + Area of large semi-circle - Area of un-shaded BEF - Area of un-shaded CHG - Area of rectangle EFGH
= 225/2 * Pi + 288*Pi - (81- 81/4*Pi)*2 - 270
= 225/2 * Pi + 288*Pi - 162 + 81/2 * Pi - 270
= 441*Pi - 432
= 953.44 square cm (Ans)

[pensiveowl]

Hi jieheng.. I've looked through your soln - thanks for taking the time. I'm wondering about this portion in red. It doesn't seem to be subtracted from the area of the squares ABFE and CDGH. Did I miss something?


http://www.positivelyquit.org/images/arc.jpg\">

[Dharma]

pensiveowl:

I need help with this problem - can someone pls help solve it - thanks


http://www.positivelyquit.org/images/math.jpg\">

http://i54.tinypic.com/2evgeac.jpg\">

[jieheng]

pensiveowl:

Hi jieheng.. I've looked through your soln - thanks for taking the time. I'm wondering about this portion in red. It doesn't seem to be subtracted from the area of the squares ABFE and CDGH. Did I miss something?


http://www.positivelyquit.org/images/arc.jpg\">

http://i52.tinypic.com/wlqeef.jpg\">

Hi pensiveowl ,

Area of un-shaded BEF = Area of un-shaded CHG =Area of square ABFE - area of small quadrant

Area of small quadrant includes Area in Red and Area in Blue

.

[raghupavithra]

i need help for this problem.

1.jennifer was given an end of year bonus. first, she gave half of her bonus plus $40 to her parents.Next, she saved half of her remaining bonus plus $30 in the bank.After that, she donated to charity half of her remaining bonus plus $20.Finally,she spent half of her remaining bonus plus $10 on some clothes.If she was left with $100,how much was her bonus?

2.Lucy wanted to buy a bag that cost $12 but did not have enough money for it.
Alan then agreed to lend her as much money as she had with her.After buying the bag,Lucy wanted to buy a pair of socks that cost$8 but did not have enough money.Randy then agreed to lend her as much money as she had with her.
After buying the pair of socks,Lucy did not have any money left with her.How much money had she at first?

[tianzhu]

Hi


I wish to begin by saying that this is not an easy question on composite figures for twelve years old kids.

As in any questions on “Circles”, it helps if a kid is able to rearrange the figure into familiar shapes.

In this question, you’ll realise that once you separate the medium semi circle(r15) from the initial figure, it becomes easier to see that the area of the shaded areas is equal to area of big semi circle(r24) + area of medium semi circle(r15) + area of small semi circle(r9) – area of rectangle ABCD. The two small quadrants (r9) add up to form a semi circle (r9).

If a kid is able to visualise this, he may skip the step on further breaking down the big semi circle, 2 quadrants and rectangle into smaller parts. Otherwise label the parts as shown in the image as it helps one to see better.

Hope this helps.

Best wishes.

http://farm7.static.flickr.com/6139/5961159714_a582e4ddac_z.jpg\">