Tutor MathsGuru: Ask me for your burning Maths questions!

[sachiko]

Thanks BigDevil. But can you please advise this part \"Lucas had 1/4 of the total amount both of them had left\"?

BigDevil:

sachiko:

Dear MathsGuru

I would appreciate if you could help me to solve the following problem sum:

Lucas and Amos had the same amount of money. Lucas spent $220 while Amos spent $112. Lucas had 1/4 of the total amount both of them had left. How much money did they have altogether at first?

Thank you.

Let me try, let me try...


http://www.postimage.org/image.php?v=Pqi5Ep9

Mathsguru, correct?

[mathsguru]

BigDevil:

sachiko:

Dear MathsGuru


I would appreciate if you could help me to solve the following problem sum:

Lucas and Amos had the same amount of money. Lucas spent $220 while Amos spent $112. Lucas had 1/4 of the total amount both of them had left. How much money did they have altogether at first?

Thank you.

Let me try, let me try...


http://www.postimage.org/image.php?v=Pqi5Ep9

Mathsguru, correct?

Hi BigDevil,

Yes! You're absolutely right! The model looks great too~~

Kudos to you,
MathsGuru

[mathsguru]

sachiko:

Thanks BigDevil. But can you please advise this part \"Lucas had 1/4 of the total amount both of them had left\"?

Hi Sachiko,

If Lucas had 1/4 of the total amount of both of them had left, ratio of Lucas' remaining amt vs. Amos' remaining amt will be 1 : 3.

Hence, 1 unit for Lucas and 3 units for Amos. Next, we add back the amounts they had spent and make both diagrams equal. Then, we can compare and find out that 2 units = $108.

Cheers,
MathsGuru

[catddy2002]

mathsguru:

catddy2002:

Hi Mathsguru,


Can check with you this question:

A teacher has some pencils.
If he give his students 2 pencils each, he has 10 pencils left.
If he give his students 3 pencils each, he has none left.
How many student he has?

Can you use a method to explain to a P4 student?
Thanks.

Hi Catddy2002,

We can use logical deduction to obtain the answer. Try explaining this to ur child:
To give each student 1 pencil more, the teacher would have to use up his remaining 10 pencils. 

Therefore, how many students can the teacher give an extra 1 pencil to if he only has 10 pencils to give away. Answer: 10 / 1 = 10 students.

Since all students receive that additional pencil, that will mean there are 10 students in all.

I use this method to solve this type of questions. It's fast and accurate and my students all find it easy to understand. Hope ur child can ace this kind of question next time. The trick is to always ask urself : To give ___ extra no. of items to each person, u'll need how many more? Sometimes u gotta add/subtract to find out how many more, depending on the question. Then, simply divide the latter by the former and answer is out.

Cheers,
MathsGuru

Hi MathsGuru,

A big thanks to you!
I've been thinking the whole night how to make my son understand.
As you mentioned before, we sometimes think too complicated, therefore, such simple way just slip out of mind. :oops:

[mathsguru]

sachiko:

Dear MathsGuru


One more question please:

Dino and Ethan have a total of 489 cards. Brad and Dino have 174 cards altogether. Ethan has 6 times as many cards as Brad. How many cards does Dino have?

Thank you.

Hi Sachiko,

Here's my solution. Hope it helps!

http://www.postimage.org/image.php?v=TsVyv1i

Cheers,
MathsGuru

[sachiko]

Thank you MathsGuru.

mathsguru:

sachiko:

Dear MathsGuru

One more question please:

Dino and Ethan have a total of 489 cards. Brad and Dino have 174 cards altogether. Ethan has 6 times as many cards as Brad. How many cards does Dino have?

Thank you.

Hi Sachiko,

Here's my solution. Hope it helps!

http://www.postimage.org/image.php?v=TsVyv1i

Cheers,
MathsGuru

[BigDevil]

mathsguru:

Hi BigDevil,


Yes! You're absolutely right! The model looks great too~~

Kudos to you,
MathsGuru

Thanks, mathsguru.

This model thing is so new to me. I would normally have used algebra to solve it. But got to get myself ready to help DD in the future. :nailbite:

[Muffins]

:rahrah: BigDevil! :rahrah:

[James Ang]

A few questions to share with the \"students\" here.


Question asked:
Q1)Find the sum of the first 100 numbers in the following number sequence.
1,2,3,4,5,6,7,8,9,1,0,1,1,1,2,1,3,1,4,1,5,.......

Q2)The Sentosa High School's telephone
number is an eight digit number.The sum of the two numbers formed from the first three digits and the last five digits respectively is 66558.The sum of the two numbers formed from the first five digits and the last three digits is 65577.Find the telephone number of the The Sentosa High School.

Q3)Placed on a table is a maths problem
89+16+69+6X+Y8+88
X and Y represents a digit.
Two students A and B sit on the opposite sides of the table facing
each other.They read the problem from
their directions and both get the same answer.What is their answer?

[mathsguru]

James Ang:

Q1)Find the sum of the first 100 numbers in the following number sequence.

1,2,3,4,5,6,7,8,9,1,0,1,1,1,2,1,3,1,4,1,5,.......

Q2)The Sentosa High School's telephone
number is an eight digit number.The sum of the two numbers formed from the first three digits and the last five digits respectively is 66558.The sum of the two numbers formed from the first five digits and the last three digits is 65577.Find the telephone number of the The Sentosa High School.

Q3)Placed on a table is a maths problem
89+16+69+6X+Y8+88
X and Y represents a digit.
Two students A and B sit on the opposite sides of the table facing
each other.They read the problem from
their directions and both get the same answer.What is their answer?

1. Make a systematic list and count the no. of numbers from 1 to 10 and 11 to 20. We'll soon deduce what is the 100th no. without having to write out every no.:
1,2,3,4,5,6,7,8,9,1,0    --> 11 no.s
1,1,1,2,1,3,1,4,1,5,1,6,1,7,1,8,1,9,2,0     --> 20 no.s
2......    --> 20 no.s
3......    --> 20 no.s
4......    --> 20 no.s
5,1,5,2,5,3,5,4,5    --> 9 no.s
Observe the patterns of the no. occurrence and we'll realise that there are 16 ones, twos, threes and fours, 11 fives and 5 sixes, sevens, eights, nines, and zeroes. Sum them up and the total is 365.

2. Use logical deduction. I'll name the digits \"a b c d e f g h\".

  a b c d e
+   f g h
  6 5 5 7 7            

a b c
+ d e f g h
6 6 5 5 8

(Urgh! Couldn't get the alignment right no matter how I try, ain't gg to waste my time adding spaces anymore u get the idea right?)

We can confidently say a = 6 and d = 6. Since 6 > 5 and a + f = 5, it makes sense that f = 9, making the sum 15. Hence, e = 5. Then h = 2. It follows that c = 6. Since c + f = 15, b = 4. Then g = 1.
Therefore, the telephone no. is 64665912.   

3. Write down the no.s read from the opposite side:
88 + 8Y + X9 + 69 + 91 + 68
If we sum up each string of no.s, we get 6X + Y8 + 262 for the original string of no.s and 8Y + X9 + 316 for the opposite string of no.s.
Possible digits are 1, 6, 8 & 9, because these no.s can still be read as no.s upside down. A bit of trial & error will reveal that the no.s are 61, 98 and 86, 19. Hence, X = 1 and Y = 9.


MathsGuru