Tutor MathsGuru: Ask me for your burning Maths questions!

[Dharma]

Vanilla Cake:

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Thks in advance for your worked solutions.Much appreciated.

http://postimage.org/image/2a7ch4pz8/

[Dharma]

Vanilla Cake:

http://postimage.org/image/1yqo8i5xg/

If A and B guessed the weight of the ball correctly,
1.\tA and B had guessed only one of the remaining 3 ( i.e. height of child, circumference of circle or volume of cup) correctly.
2.\tC had guessed the weight of the ball wrongly.
3.\tC had guessed 2 of the 3 (i.e. height, circumference or volume) correctly.
4.\tSince A and C had guessed the same values for both circumference and volume; and A had guessed the weight correctly, A and C must have guessed either the circumference correctly.
5.\tIf that is the case; C must have guessed the height of the child correctly too to get 2 correct guesses.

If C guessed the weight of the ball correctly
1.\tC must guess only one of the remaining 3 (i.e. height, circumference or volume) correctly.
2.\tBut A and C guessed the same value for circumference and volume. So, both A and C made the wrong guess for these values otherwise C would have gotten 3 guesses correct.
3.\tSo, C had guessed the height of the child correctly.

Height of the child, x = 80cm

[MathIzzzFun]

duplicate. deleted

[MathIzzzFun]

Vanilla Cake:

http://postimage.org/image/2oi1t1xac/



Thks in advance for your worked solutions.Much appreciated.

Hi

2 alternate methods to solve this :lol:


http://postimage.org/image/cut4b7s4/



http://postimage.org/image/cuy2x99g/

cheers.

[Dharma]

Vanilla Cake:

http://postimage.org/image/10ysrailg/

http://postimage.org/image/3rbcpr0k/

[wahwah]

Hi,

Need help with the following questions. Many thanks in advance.

The 100th term of the sequence 1/3 , 1/2 , 5/9 , 7/12, 3/5, 11/18, …is
(1)167/270
(2)199/300
(3)67/101
(4)287/312
(5)none of the above


In the sequence of fractions 1/1, 2/1, 1/2, 3/1, 2/2, 1/3, 4/1, 3/2, 2/3, 1/4, 5/1, 4/2, 3/3, 2/4, 1/5, …, fractions equivalent to any given fraction occur many times. For example, fractions equivalent to 1/2 occur for the first two times in position 3 n 14. In what positions is the fifth occurrence of a fraction equivalent to 3/7?

(1)1208
(2)1209
(3)1210
(4)1211
(5)none of the above.

[MathIzzzFun]

wahwah:

Hi,

Need help with the following questions. Many thanks in advance.

The 100th term of the sequence 1/3 , 1/2 , 5/9 , 7/12, 3/5, 11/18, ...is
(1)167/270
(2)199/300
(3)67/101
(4)287/312
(5)none of the above


In the sequence of fractions 1/1, 2/1, 1/2, 3/1, 2/2, 1/3, 4/1, 3/2, 2/3, 1/4, 5/1, 4/2, 3/3, 2/4, 1/5, ..., fractions equivalent to any given fraction occur many times. For example, fractions equivalent to 1/2 occur for the first two times in position 3 n 14. In what positions is the fifth occurrence of a fraction equivalent to 3/7?

(1)1208
(2)1209
(3)1210
(4)1211
(5)none of the above.

Q1.
The 100th term of the sequence 1/3 , 1/2 , 5/9 , 7/12, 3/5, 11/18, ...is
... rewrite 1/2 = 3/6, 3/5 = 9/15 we have the sequence as
1/3 , 3/6 , 5/9 , 7/12, 9/15, 11/18. .. this sequence now looks less intimidating...
numerator = odd numbers = 2n-1 where n= 1,2,3.....
denominator = multiple of 3 = 3n where n=1,2,3.....

for 100th term
>> numerator = 2 x 100 - 1 = 199
>> denominator = 3 x 100 = 300

100th term = 199/300

Q2. In the sequence of fractions 1/1, 2/1, 1/2, 3/1, 2/2, 1/3, 4/1, 3/2, 2/3, 1/4, 5/1, 4/2, 3/3, 2/4, 1/5, ..., fractions equivalent to any given fraction occur many times. For example, fractions equivalent to 1/2 occur for the first two times in position 3 n 14. In what positions is the fifth occurrence of a fraction equivalent to 3/7?

Regroup the terms as
1/1 - 1st group, 1 term

2/1, 1/2 ==> 2nd group, 2 terms >> sum of numerator and denominator = 3. numerator in decending order start from 2 down to 1, denominator in ascending order from 1 to 2 and denotes the position of the term in the group


3/1, 2/2, 1/3 ==> 3rd group, 3 terms >> sum of numerator and denominator = 4. numerator in decending order start from 3 down to 1, denominator in ascending order from 1 to 3 and denotes the position of the term in the group


4/1, 3/2, 2/3, 1/4 ==> 4th group, 4 terms >> sum of numerator and denominator = 5. numerator in decending order start from 4 down to 1, denominator in ascending order from 1 to 4 and denotes the position of the term in the group

5/1, 4/2, 3/3, 2/4, 1/5 ==> 5 terms >> sum of numerator and denominator = 6. numerator in decending order start from 5 down to 1, denominator in ascending order from 1 to 5 and denotes the position of the term in the group

Next, pattern for occurence of equivalent fractions
1/2 = 3rd term in sequence. note that numerator = 1>> 1st occurence
2/4 = 14th term in sequence. note that numerator = 2 >> 2nd occurrence. note that sum of numerator and denominator = 6 so this is in the 5th group with 5 terms ie numerator from 5 to 1, denominator from 1 to 5, and this is 4th term in this group since denominator is 4. Number of terms in the 1st four groups = 1 + 2 + 3 + 4 =10, 10 + 4 = 14, so this is the 14th term.

For 3/7, the fifth occurrence = 15/35 (multiply both numerator and denominator by 5)

15/35 - sum of numerator and denominator is 50, so this is in the 50-1 = 49th group which has 49 terms in the group. note denominator is 35 so this is the 35th term in the group.

Position of 15/35 in the sequence = sum of terms in the 1st 48 groups + 35

Number of terms of 1st 48 groups
= 1 +2 + 3 + 4 + ... + 46 + 47 + 48
= 1176

1176 + 35 = 1211

so 5th occurrence of 3/7 = 15/35 = 1211 th term in sequence

cheers.

[wahwah]

Hi MathIzzzFun,


Thanks for the solution! Really appreciate your kind help!

[MathIzzzFun]

wahwah:

Hi MathIzzzFun,


Thanks for the solution! Really appreciate your kind help!

you are welcome :lol:

cheers.

[YANNG]

I am looking for a good Math home tutor near Tampines to coach my daughter who is in P5 this year. Anyone with good contact ?