Q&A - PSLE Math

[Belle2011]

Dear Brenda10,

Thanks very much for your help.

Cheers,
Belle

[Belle2011]

Brenda10:

Belle2011:

Hi,

I need some help again.

(1) Dolly had 80 more stickers than Jenny. Dolly gave 25% of her stickers to Jenny. Jenny in return gave 60% of her stickers to Dolly. In the end, Dolly had 100 stickers more than Jenny. How many stickers did Dolly have at first?

(model ans: 116 stickers)
Thanking you in advance.

Hi, this question was from Nan Hua 2010 CA1 P2 Q18.

25%= 1/4, 60% = 3/5

1/4=5/20, 3/5 = 12/20
80 x 5/20 = 20, 20 x 12/20 = 12
80 - 20 = 60, 20 - 12 = 8


4u+ 60 + 12 = 100 + 8
4u + 72 = 108
4u = 108 - 72
4u = 36

Dolly: 4u + 80
36 + 80 = 116


Thank you

Can anybody offer some detailed explanation?

What does 80-20 = 60, 20-12 = 8 mean?
What does 4u+ 60 + 12 = 100 + 8 mean?
Thanks.

[Belle2011]

Brenda10:

Belle2011:

(2) Julian had 300 more cards than Faizal. Julian gave 3/5 of his cards to Faizal. Faizal then gave 1/4 of the total number of what he had then to Julian. In the end, Faizal had 300 more cards than Julian. How many cards did Julian have at first?

(model ans: 1125)

Hi, this question was from NY 2010 CA1 P2 Q17.

3/5, 1/4

12/20 , 5/20

300 x 12/20 = 180, 180 x 5/20 = 45
300- 180 = 120, 180 - 45 = 135

2u = 120 + 45 + 300 = 135
2u = 330
1u = 165

Julian: 5u + 300
5 * 165 + 300 = 1125

Thank you

Similarly, can anybody offer some detailed explanation?
What does 300- 180 = 120, 180 - 45 = 135 mean?
How to get 2u = 120 + 45 + 300 = 135 ?
Thanks.

[Brenda10]

Belle2011:

Brenda10:

[quote=\"Belle2011\"]
(2) Julian had 300 more cards than Faizal. Julian gave 3/5 of his cards to Faizal. Faizal then gave 1/4 of the total number of what he had then to Julian. In the end, Faizal had 300 more cards than Julian. How many cards did Julian have at first?

(model ans: 1125)

Hi, this question was from NY 2010 CA1 P2 Q17.

3/5, 1/4

12/20 , 5/20

300 x 12/20 = 180, 180 x 5/20 = 45
300- 180 = 120, 180 - 45 = 135

2u = 120 + 45 + 300 - 135
2u = 330
1u = 165

Julian: 5u + 300
5 * 165 + 300 = 1125

Thank you

Similarly, can anybody offer some detailed explanation?
What does 300- 180 = 120, 180 - 45 = 135 mean?
How to get 2u = 120 + 45 + 300 = 135 ?

Thanks.[/quote]Oh there is a typing error, should be:

2u = 120 + 45 + 300 -135

Sorry as I just transferred dd's working and can't help in explanation. Hopefully someone else can help.

[Dharma]

Brenda10:

Belle2011:

[quote=\"Brenda10\"]
Hi, this question was from NY 2010 CA1 P2 Q17.

3/5, 1/4

12/20 , 5/20

300 x 12/20 = 180, 180 x 5/20 = 45
300- 180 = 120, 180 - 45 = 135

2u = 120 + 45 + 300 - 135
2u = 330
1u = 165

Julian: 5u + 300
5 * 165 + 300 = 1125

Thank you

Similarly, can anybody offer some detailed explanation?
What does 300- 180 = 120, 180 - 45 = 135 mean?
How to get 2u = 120 + 45 + 300 = 135 ?

Thanks.

Oh there is a typing error, should be:

2u = 120 + 45 + 300 -135

Sorry as I just transferred dd's working and can't help in explanation. Hopefully someone else can help.[/quote]Sorry, just another way of presentation.

Julian gave 3/5 of his cards to Faizal
Julian : 100u – 60u = 40u
Faizal : (100u – 300) + 60u = 160u – 300

Faizal gave ¼ of his cards to Julian
Julian : 40u + (40u – 75) = 80u - 75
Faizal : (160u – 300) – (40u – 75) = 120u – 225

Difference = 120u – 225 – (80u – 75) = 300
40u = 300 + 150 = 450

No. of cards Julian had at first = 100u = 450/40 x 100 = 1125

[Belle2011]

Dharma:

Julian gave 3/5 of his cards to Faizal

Julian : 100u – 60u = 40u
Faizal : (100u – 300) + 60u = 160u – 300

Faizal gave ¼ of his cards to Julian
Julian : 40u + (40u – 75) = 80u - 75
Faizal : (160u – 300) – (40u – 75) = 120u – 225

Difference = 120u – 225 – (80u – 75) = 300
40u = 300 + 150 = 450

No. of cards Julian had at first = 100u = 450/40 x 100 = 1125

Hello Dharma,
You have \"assigned\" 100u to Julian and thus Faizal has 100u-300 etc
Thank-you for your explanation.
BTW, can you offer a similar explanation/working for the other question mentioned earlier, please?
Cheers,
Belle.

[Dharma]

Belle2011:

Dharma:

Julian gave 3/5 of his cards to Faizal

Julian : 100u – 60u = 40u
Faizal : (100u – 300) + 60u = 160u – 300

Faizal gave ¼ of his cards to Julian
Julian : 40u + (40u – 75) = 80u - 75
Faizal : (160u – 300) – (40u – 75) = 120u – 225

Difference = 120u – 225 – (80u – 75) = 300
40u = 300 + 150 = 450

No. of cards Julian had at first = 100u = 450/40 x 100 = 1125

Hello Dharma,
You have \"assigned\" 100u to Julian and thus Faizal has 100u-300 etc
Thank-you for your explanation.
BTW, can you offer a similar explanation/working for the other question mentioned earlier, please?
Cheers,
Belle.

Dolly gave 25% of her stickers to Jenny
Dolly : 100u – 25u = 75u
Jenny : (100u – 80) + 25u = 125u – 80

Jenny gave 60% of her stickers to Dolly
Dolly : 75u + (75u – 48 ) = 150u - 48
Jenny : (125u – 80) – (75u – 48 ) = 50u – 32

Difference = (150u – 48 ) – (50u – 32) = 100
100u – 16 = 100
100u = 116

No. of stickers Dolly had at first = 100u = 116

[Brenda10]

Dharma:

Dolly gave 25% of her stickers to Jenny

Dolly : 100u – 25u = 75u
Jenny : (100u – 80) + 25u = 125u – 80

Jenny gave 60% of her stickers to Dolly
Dolly : 75u + (75u – 48 ) = 150u - 48
Jenny : (125u – 80) – (75u – 48 ) = 50u – 32

Difference = (150u – 48 ) – (50u – 32) = 100
100u – 16 = 100
100u = 116

No. of stickers Dolly had at first = 100u = 116

Hi Dharma

Thank you for providing another method of doing as dd can also learn another way of solving problem.

[Belle2011]

Dharma:

Dolly gave 25% of her stickers to Jenny

Dolly : 100u – 25u = 75u
Jenny : (100u – 80) + 25u = 125u – 80

Jenny gave 60% of her stickers to Dolly
Dolly : 75u + (75u – 48 ) = 150u - 48
Jenny : (125u – 80) – (75u – 48 ) = 50u – 32

Difference = (150u – 48 ) – (50u – 32) = 100
100u – 16 = 100
100u = 116

No. of stickers Dolly had at first = 100u = 116

Dear Dharma,
Thanks very, very much for your help.
Cheers,
Belle

[tianzhu]

[quote]4u+ 60 + 12 = 100 + 8

4u + 72 = 108
4u = 108 - 72
4u = 36[/quote][quote]2u = 120 + 45 + 300 - 135
2u = 330
1u = 165[/quote]Hi Brenda10

I am curious to know how your dd got to these steps.Did she use Model Drawing or Units Method?

Best wishes