Tutor MathsGuru: Ask me for your burning Maths questions!

[tinasen]

Dear MathGuru,

It was my son who posted these questions since he could not get a satisfactory help from his own private tutor.
Your solution with explanations are mind blowing. Hats off to you!
I'm sure many struggling parents like me are benefiting from this forum.
God bless for this volunteer service.

Wish you a very Happy and prosperous Rabbit Year.

- Thanks
Tinasen

mathsguru:

charsen:

Hi Mathguru,

Kindly help me with my math problem.
Colin and Rosdin had the same amount of pocket money. Each day, Colin spent $12 and Rosdin spent $15. When Rosdin had $18 left Colin had 5 times as much money left as Rosdin. How much was each boy's pocket money?

It will be of great help if you show me the solution by model method.

TIA
charsen

Hi Charsen,

Happy CNY to you! Saw your PM and I've have done up the solutions but can't send them to you over PM, hence posting them here.

Hope they help!

Cheers,
MathsGuru

http://postimage.org/image/4if5r8o4/

http://postimage.org/image/4iigtxno/

http://postimage.org/image/4ilrwmn8/

[tinasen]

Hi MathGuru,

For Q3 \"Millie and Ronnie had a total of $338. After Millie saved $49 and Ronnie spent half of her money,they both had the same amount of money. How much did Millie have at first?\"
As it is stated Millie \"Saved\" $49 I got the following answer which is diffrent from yours. May be I'm wrong.

2*49 = 98
338-98 = 240
240/2 = 120
The final answer I got was 120.

- Tinasen

mathsguru:

charsen:

Hi Mathguru,

Kindly help me with my math problem.
Colin and Rosdin had the same amount of pocket money. Each day, Colin spent $12 and Rosdin spent $15. When Rosdin had $18 left Colin had 5 times as much money left as Rosdin. How much was each boy's pocket money?

It will be of great help if you show me the solution by model method.

TIA
charsen

Hi Charsen,

Happy CNY to you! Saw your PM and I've have done up the solutions but can't send them to you over PM, hence posting them here.

Hope they help!

Cheers,
MathsGuru

http://postimage.org/image/4if5r8o4/

http://postimage.org/image/4iigtxno/

http://postimage.org/image/4ilrwmn8/

[mathsguru]

tinasen:

Hi MathGuru,

For Q3 \"Millie and Ronnie had a total of $338. After Millie saved $49 and Ronnie spent half of her money,they both had the same amount of money. How much did Millie have at first?\"
As it is stated Millie \"Saved\" $49 I got the following answer which is diffrent from yours. May be I'm wrong.

2*49 = 98
338-98 = 240
240/2 = 120
The final answer I got was 120.

- Tinasen

Hi Tinasen,

Sorry, I've read the question wrongly! Haha...instead of saved $49, I read it as soent $49! Ooopsss...No wonder I thought my answer looks quite weird with fraction in it! Correct answer should be $80.

Here's the amended solution:

http://postimage.org/image/1ssi1dbr8/

Cheers,
MathsGuru

[tinasen]

Thank you Math Guru.

mathsguru:

tinasen:

Hi MathGuru,
For Q3 \"Millie and Ronnie had a total of $338. After Millie saved $49 and Ronnie spent half of her money,they both had the same amount of money. How much did Millie have at first?\"
As it is stated Millie \"Saved\" $49 I got the following answer which is diffrent from yours. May be I'm wrong.

2*49 = 98
338-98 = 240
240/2 = 120
The final answer I got was 120.

- Tinasen

Hi Tinasen,

Sorry, I've read the question wrongly! Haha...instead of saved $49, I read it as soent $49! Ooopsss...No wonder I thought my answer looks quite weird with fraction in it! Correct answer should be $80.

Here's the amended solution:

http://postimage.org/image/1ssi1dbr8/

Cheers,
MathsGuru

[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!

[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.

[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