Q&A - PSLE Math

[mrswongtuition]

Hershey:

1) Albert and Benny had $282. Benny had $4 more than Albert. Benny spent 1/2 as much as Albert and was left with twice as much as Albert. How much did Benny spent?

At first: Benny had $4 more than Albert. They had $282.
A [--------] ```` }Total
B [--------][ 4 ]` }$282

Benny spent 1/2 as much as Albert and was left with twice as much as Albert.
[---] = left
[___] = spent

A [__][__][------]
B [__][------][------]
` ` ` ` ` ` ` ` ` [ 4]

Which means that....
1 unit of what was left is greater than 1 unit of what was spent by $4.

Redrawing it:
[++] = 1 unit of what was spent

A [++][++][++][4] ` `} Total
B [++][++][4][++][4] } 282

6 units = 282 - 4 - 4 - 4 = 270
1 unit = 270/6 = 45

Benny spent $45.

Hershey:

2) The ratio of the number of stickers Alex had to the number of stickers Beng Han had was 1:3. After each of them received 25 stickers, the ratio became 3:4. How many stickers did they have altogether at first?

A : B
1 : 3
+25:+25
3 : 4

Note: Since each of them received the same amount of stickers, the DIFFERENCE between the number of stickers at first and after remains the same.

A : B
1 : 3
Differece: 2 units
______________
+25:+25
______________
3 : 4
Difference: 1 unit

Multiply to make the difference in units the same:

A : B
1 : 3
Differece: 2 units (no change)
______________
+25:+25
______________
3 x 2 : 4 x 2
6 : 8
Difference: 1 unit x 2 = 2units

Comparing Alex's 6 units of stickers after receiving 25 stickers and his 1 unit of stickers at first...
6 - 1 = 5
5 units -> 25 stickers
1 unit -> 5 stickers

Total stickers at first: 1 + 3 = 4 units
4 units -> 4 x 5 = 20 stickers

[atutor2001]

chrisu:

Thanks to all for responding to this post. My daughter came back yesterday evening and told me that the teacher and the Maths HOD agreed to accept both 225 and 450 as answer since the question is ambiguous.


The answer is 225 if comparison is made after the 1/3 and 1/5 is given to Rahmad. The answer will be 450 if the comparison is made before the 1/3 and 1/5 is given to Rahmad.

As for proving of Adam = 450;
If Adam = 450, Rahmad will be 370.
If Adam gives 1/3 of 450 to Rahmad,
Rahmad will get : 370 + 150 = 520.
520 - 450 = 70 (which is 70 more than Adam before the 1/3 is given out).

If Adam gives 1/5 of 450 to Rahmad,
Rahmad will get : 370 + 90 = 460.
460 - 450 = 10 (which is 10 more than Adam).

The school's HOD ought to be skinned. Nothing in the question (based on what is given here) hinted that the comparison is to be made between \"after\" of Rahmad and \"before\" of Adam.

This is a common question and the school should know. A typical example of blindly following answer key with no confident to decide that the answer 450 is wrong.

[Sun_2010]

atutor2001:

chrisu:

Thanks to all for responding to this post. My daughter came back yesterday evening and told me that the teacher and the Maths HOD agreed to accept both 225 and 450 as answer since the question is ambiguous.


The answer is 225 if comparison is made after the 1/3 and 1/5 is given to Rahmad. The answer will be 450 if the comparison is made before the 1/3 and 1/5 is given to Rahmad.

As for proving of Adam = 450;
If Adam = 450, Rahmad will be 370.
If Adam gives 1/3 of 450 to Rahmad,
Rahmad will get : 370 + 150 = 520.
520 - 450 = 70 (which is 70 more than Adam before the 1/3 is given out).

If Adam gives 1/5 of 450 to Rahmad,
Rahmad will get : 370 + 90 = 460.
460 - 450 = 10 (which is 10 more than Adam).

The school's HOD ought to be skinned. Nothing in the question (based on what is given here) hinted that the comparison is to be made between \"after\" of Rahmad and \"before\" of Adam.

This is a common question and the school should know. A typical example of blindly following answer key with no confident to decide that the answer 450 is wrong.

Agreed !
The question as interpreted by the school is flawed.

[tianzhu]

chrisu:

Maybe the school should inform the publisher that there are 2 answers to the question.

Hi

Where is your question from?

You may want to write to the publisher to clarify.

Best wishes

[chrisu]

The question is from MyPal workbook where a number of the parents' kids are using too. Those students from other schools are also given the 450 as answer and not too sure if there is any feedback from their parents.

tianzhu:

chrisu:

Maybe the school should inform the publisher that there are 2 answers to the question.

Hi

Where is your question from?

You may want to write to the publisher to clarify.

Best wishes

[tianzhu]

chrisu:

The question is from MyPal workbook where a number of the parents' kids are using too. Those students from other schools are also given the 450 as answer and not too sure if there is any feedback from their parents.

Hi

Questions involving two cases or double if are common in primary maths.

Let your kid go through these questions, do we compare with the original quantity or remaining?

1) Wawa had some red and blue stickers. If 72 red stickers were removed, the ratio of the number of red stickers to that of the blue stickers would be 1 : 2. If 180 blue stickers were removed instead, the ratio would become 5 : 1. How many red stickers were there?

2) There are some red pins and blue pins in a box. If one of the red pin is removed, the number of red pins left will be 1/7 of the total number of pins left. If two blue pins are removed, the number of red pins will be 1/5 of the total number of pins left. How many pins are there in the box?

3) If Mark gives Lenny 14 stickers, he will have the same number of stickers as Lenny. If Lenny gives 10 stickers to Mark, the ratio of the number of stickers Lenny has to that of Mark will be 2: 5. How many stickers does Mark have?

Best wishes

[James Ang]

When Larry's age was twice Henry's age, Don's age was 27. When Don's age was twice Larry's age, Henry's age was 15. What was Henry's age when Don was 58 years old ?



Let me show how a P5 student would do to solve by drawing a model. (Remember that P5 students do not know any algebra!)


L [][]+[31]
H []+[31]
D [27]+[31] = 58

L [15][] + [][16]
H [15] +[][16]
D [15][][15][] + [][16] = 58

from above
D [15][][15][] + [][16] = 58
[][][] = 58-15-15-16 = 12
[]=4

Therefore Henry = [15] +[][16] = 15+4+16 = 35 years old.

A picture speaks a thousand words!

[Belle2011]

Hello,

Can somebody help me with this problem?

F, L and W each owned a collection of comics. The total collected owned by L and W was 3/2 as many comics as F owned. L owned 4/5 as many comics as the total collection owned by F and W. If W owned 169 fewer comics than L, how many comics must F and L each give to W in order for the 3 girls to have the same number of comics?

Thank-you.

Cheers,
Belle

[iFruit]

Belle2011:

Hello,

Can somebody help me with this problem?

F, L and W each owned a collection of comics. The total collected owned by L and W was 3/2 as many comics as F owned. L owned 4/5 as many comics as the total collection owned by F and W. If W owned 169 fewer comics than L, how many comics must F and L each give to W in order for the 3 girls to have the same number of comics?

Thank-you.

Cheers,
Belle

W = L - 169

F = 2/3 ( W + L) = 2/3 (L-169 + L) = 2/3 (2L -169)

5L/4 = W+F = (L - 169) + 2/3 (2L -169) = (3L - 3x169 + 4L -2x169)/3 = (7L -5x169)/3

15L = 28L -20x169----->13L = 20x169----> L = 20x13 = 260

So

W = L -169 = 260 -169 = 91

F = 2/3 (91+260) = 2/3 (351) = 234

(L+W+F)/3 = (260+234+91)/3 = 585/3 = 195

So,

L must give 260-195 = 65 to W

F must give 234 -195 = 39 to W

HTH.

[Dharma]

Belle2011:

Hello,

Can somebody help me with this problem?

F, L and W each owned a collection of comics. The total collected owned by L and W was 3/2 as many comics as F owned. L owned 4/5 as many comics as the total collection owned by F and W. If W owned 169 fewer comics than L, how many comics must F and L each give to W in order for the 3 girls to have the same number of comics?

Thank-you.

Cheers,
Belle

F : L + W = 2 : 3 = 18 : 27
L : F + W = 4 : 5 = 20 : 25

L => 20u
F => 18u
W => 7u

20u – 7u = 169
13u = 169
1u = 13

No. of comics that F gives to W = 18u – 15u = 3u = 3 x 13 = 39
No. of comics that L gives to W = 20u – 15u = 5u = 5 x 13 = 65