Tutor MathsGuru: Ask me for your burning Maths questions!

[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

[James Ang]

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

correct.
Q3 answer is 421

Wonder why students are given these primary questions in school, perhaps to really differentiate those who are really good from average ones.

[happies]

Hi mathsguru,


Have been scratching my head for this question:(

Peter spent 1/4 of his money and an additional $3 on a shirt. He then spent 2/5 of the remaining money and an additional $6 on a pair of pants. Given that he was left with $24, how much money did Peter have at first?

Thanks a lot.

[ooptimizer]

$70.67

[happies]

thanks ooptimizer:D


i got this answer too, but not very sure as the answer looks a bit unusual to me…thanks again

[mathsguru]

happies:

Hi mathsguru,


Have been scratching my head for this question:(

Peter spent 1/4 of his money and an additional $3 on a shirt. He then spent 2/5 of the remaining money and an additional $6 on a pair of pants. Given that he was left with $24, how much money did Peter have at first?

Thanks a lot.

Hi Happies and Ooptimizer,

Hi-5! Got the same answer as both of u.

Cheers,
MathsGuru