Tutor MathsGuru: Ask me for your burning Maths questions!

[lostbunny]

kwcllf:

Hi,


Please help with the following question.

Peter, Mary and Sam have a total of $1,200. If Peter gave them $25 each, Peter and Mary would have a total amount which was $10 less than Sam. Given that Sam originally had 4 times as much money as Mary, how much did Peter have originally?

Thanks!

Kwcif,

My DH insist I post this answer that he worked out.

P + M -10= S = 1200
595 = 605 ( this is the only combination where the diff is by 10)

S=605-25=580s/4=145M
1200-580S-145M= 475P

Prove
475P-50=425P
145M+25=170M
575PM
580S+25=605S

Maths guru, is this correct?

[autolycus]

kwcllf:

Hi,


Please help with the following question.

Peter, Mary and Sam have a total of $1,200. If Peter gave them $25 each, Peter and Mary would have a total amount which was $10 less than Sam. Given that Sam originally had 4 times as much money as Mary, how much did Peter have originally?

Thanks!

Originally:
Mary has $M
Sam has 4 x $M
Peter has $1,200 - 5 x $M

Then Peter gets generous.

This becomes:
Peter has $1200 - 5 x $M - $25 - $25
Mary has $M + $25
Sam has 4 x $M + $25

But to put it another way...

Sam also has Peter's money + Mary's money + $10
= $1200 - 5 x $M - $50 + $M + $25 + $10
= $1200 - $50 + $25 + $10 - 5 x $M + $M
= $1185 - 4 x $M

So Sam's money can be expressed in 2 ways but must be the same:

4 x $M + $25 = $1185 - 4 x $M
4 x $M + $25 + 4 x $M = $1185
8 x $M = $1185 - $25 = $1160

So $M = $1160/8 = $145

Conclusion:
Mary started with $M = $145
Sam started with 4 x $M = 4 x $145 = $580
Peter had the balance = $1200 - $580 - $145 = $475

After Peter gave them each $25,
Mary had $170
Sam had $605
Peter had $425

[Yu Xuan]

rain29:

Hi,


I need help for the following questions with drawing model.

1) Tom and Jerry had equal amount of money at first. After Tom spent $8 and Jerry spent $32. Tom had 4 times as much as Jerry. How much did Tom have at first?


2) John had $130 and Elicia had $88 at first. After they each spent an equal amount of money. John had 4 times as much money as Elicia. How much money did each of them spend?

Thanks in advance.

Hi

Question 1

Tom --> [ ][ ][ ][ ][$8]
Jery --> [ ][....$32.....]

3 units --> $32 - $8 = $24
1 unit --> $24 / 3 = $8
4 units --> $8 * 4 = $32

$32 + $8 = $ 40

Question 2

Jo --> [Spent][ ][ ][ ][ ]
El --> [Spent][ ]

3 units --> $130 - $88 = $42
1 unit --> $42 / 3 = $14

Using Elicia;
$88 - $14 = $ 74

[Yu Xuan]

kwcllf:

Hi,


Please help with the following question.

Peter, Mary and Sam have a total of $1,200. If Peter gave them $25 each, Peter and Mary would have a total amount which was $10 less than Sam. Given that Sam originally had 4 times as much money as Mary, how much did Peter have originally?

Thanks!

Hi

After transfer;
Sam --> 4 units + $25
Mary --> 1 unit + $25

Since Peter & Mary would have $10 less than Sam, Peter & Mary should have;
4 units + $25 - $10 = 4 units + $15

If Mary has 1 unit + $25, then Peter should have;
4 units + $15 - 1 unit - $25 = 3 units - $10

To find out what Peter started off with, we need to add back the $50 which he transferred to Sam & Mary;
3 units - $10 + $50 = 3 units + $40

Using the $1200 which 3 of them started off with;
4u + 1u + 3u + $40 --> $1200
8u --> $1200 - $40 = $1160
1u --> $1160 / 8 = $145

Peter at first --> 3u + 40 = [ 3*$145 ] + $40 = $475

[rain29]

Hi Yu Xuan,


Thanks for your help.

I can get the answer but my daughter dun understand with my explanation. I will explain to her using your method, hope she can understand better.

[Yu Xuan]

rain29:

Hi Yu Xuan,


Thanks for your help.

I can get the answer but my daughter dun understand with my explanation. I will explain to her using your method, hope she can understand better.

Hi Rain

The pleasure is mine. Nice day.

Yu Xuan

[kwcllf]

Hi All,


Thanks for the great help. I managed to do it using the Model method as my P5 kid can understand better.

Please see below (Sorry, can’t get it into alignment)

M--------[135][10]

S--------[135][10][135][10][135][10][135][10][15][10]
P+M---- [135][10][135][10][135][10][135][10][15]


From the above model (taking into account of S & P+M only):

$1200 – (9 x $10) – (2 x$ 15) = $1080
$1080 ÷ 8 = $135

Therefore originally,
Sam = (4 x $135) + (4 x $10) = $580
Mary = $135 + $10 = $145
Peter = $(1200 – 580 – 145 ) = $475

[andante]

Pls help for the following question. I have solved it using algebra simultaneous equations but I heard that the pupils cannot use this method to solve during PSLE exam or else marks will be deducted.



20% of the number of balls Kyle had is equal to the 35% of the number Pauline had. After Kyle sold another 30 marbles and Pauline bought 20 marbles, 30% of the number of marbles Kyle had is equal to the 50% of the number Pauline had. What is the number of marbles each of them had at first?

Thanks in advance

[meimeitan]

Hi Maths Guru


There is a Math question as following:

There were 12 more girls than boys in a club. 1/3 of the girls and 1/4 of the boys took part in a competition. Among those who took part in the competition, there were 6 more girls than boys. What fraction of the club members who did not take part in the competition were boys?

May I know the meaning of "What fraction of the club members who did not take part in the competition were boys.?" The denominator should be the whole club members or the club members who did not join the competition.

Thanks

[ADoc]

andante:

...using algebra simultaneous equations but I heard that the pupils cannot use this method to solve during PSLE exam or else marks will be deducted...

Hi there! Sorry for the repetition. Since we have \"new\" PSLE moms & dads every year, guess this piece of info would serve well to many.

Here's an excerpt from the \"Forum Letter Replies\" by MOE & SEAB on \"Different Approaches Taught for Mathematics Techniques\":

\"....While pupils are not required to use algebra to solve word problems in the PSLE Mathematics, they are also not restricted to the use of any one particular method. In the marking of PSLE Mathematics, all mathematically correct solutions are acceptable and there is no loss of marks if a correct algebraic method is used.\"
See http://www.moe.gov.sg/media/forum/2007/20070217.htm

Hope this clarifies your doubt. Notwithstanding MOE's and SEAB's endorsement, parents need to ensure their kids are able to internalise and apply what you have explained / taught them about algebraic solutions, instead of merely understanding. Else they may be extremely confused. There's a good reason why the primary curriculum limits the extent of algebraic teachings; not all students are able to grasp the seemingly abstract concepts of x, y, & z, even though algebra is already masked in the form of Models & Units.

Just a quick suggestion: More often than not, the algebraic approach can be \"transformed\" to the model approach. For example, instead of saying \"let x be...\", we can always draw a certain length of model to represent the same thing. Remember that model is algebra in disguise.

Of cos, if your kid is quick at grasping advanced concepts, do go ahead and use algebra. I have taught my students algebra and encourage those confident enough to use them in PSLE. Confirmations with past students using algebra obtained A* with no problems at all. Perhaps this can be another instance to nullify the hear-say that algebra will result in loss of marks.

cheers!
ADoc