Tutor MathsGuru: Ask me for your burning Maths questions!

[trytry]

VC’s mum, thanks for your link.


atutor2001, thanks for your clear and helpful explanation.

[Dharma]

trytry:

\t\t\t\t\t\t

\t\t
2. There are 5 members in John's family : Father, Mother, elder sister Helen, John and younger sister Lucy. Just before Lucy was borned, the average age of the family was 19 yrs old and the age of John's father is same as the sum of ages of the rest of family. 2 years ago, the average age of the family was 35.2 yrs and the age of John's mother was 8 years more than the sum of ages of John and Lucy. The current average age of the family, excluding Helen, is 39.5 years. Find the present age of John.


Thanks.

Before Lucy was born
F + M + H + J = 19 x 4 = 76

F = M + H + J
F = 38
M + H + J = 38

Just after Lucy was born
F + M + H + J + L = 76
Average age = 76/5 = 15.2

2 years ago
Lucy’s age = 35.2 – 15.2 = 20
Father’s age = 38 + 20 = 58
M = J + L + 8
M = J + 28

Now
F + M + J + L = 39.5 x 4 = 158
M + J = 158 – 60 – 22 = 76

2 yrs ago
M + J = 76 – 4 = 72 ---------------- ( 1 )
M – J = 28 ----------------------------( 2 )
(1 ) – (2 )
2J = 72 - 28 = 44
J = 22

John’s age now = 22 + 2 = 24 yrs old

[Dharma]

trytry:

Q1. 20 students took a test. The teacher ranked them from the highest score (1st) to the lowest score (20th). The top 10 students had an average of 92 marks and the next 10 students had an average of 80 marks. Also, the top 5 students had an average score that was 12 marks higher than the average of next 15 students. Find the lowest possible score of the student in the 20th rank. \t\t\t\t\t\t\t

Thanks.

Top 10 students : Ave = 92
Top 11th to 20th student : Ave = 80

5(1u + 12) + 15(1u) = 920 + 800 = 1720
20u = 1660
1u = 83
Top 5 students : Ave = 83 + 12 = 95
Top 6th to 10th students : Ave = (920 – 5(95)/5 = 89

RANKING
1. 97
2. 96
3. 95
4. 94
5. 93
6. 91
7. 90
8. 89
9. 88
10. 87

86 + 85 + …. + 78 = [ 4(78 + 85) + 86] = 738

Lowest possible score = (80 x 10 ) – 738 = 62

[Muffins]

thanks Dharma, for your crystal clear explanation!!!!

[Dharma]

Muffins:

thanks Dharma, for your crystal clear explanation!!!!

No worries, mate.

[trytry]

Thanks Dharma.

[2DMommy]

Mr Muthu bought a refrigerator worth $1450 with his monthly salary. After spending 1/6 of his remaining salary on a digital camera, he had 5/8 of his salary left. What was Mr Muthu’s salary?

[iFruit]

2DMommy:

Mr Muthu bought a refrigerator worth $1450 with his monthly salary. After spending 1/6 of his remaining salary on a digital camera, he had 5/8 of his salary left. What was Mr Muthu's salary?

Salary = s

(s-1450)5/6 = 5s/8

8s - 1450x8 = 6s

s = 5800

[2DMommy]

iFruit:

2DMommy:

Mr Muthu bought a refrigerator worth $1450 with his monthly salary. After spending 1/6 of his remaining salary on a digital camera, he had 5/8 of his salary left. What was Mr Muthu's salary?

Salary = s

(s-1450)5/6 = 5s/8

8s - 1450x8 = 6s

s = 5800

Thank you for working out the answer. Can work out without using equation?

[kancheongmum]

2DMommy:

Mr Muthu bought a refrigerator worth $1450 with his monthly salary. After spending 1/6 of his remaining salary on a digital camera, he had 5/8 of his salary left. What was Mr Muthu's salary?

Hi 2DMommy


I do not know how to post the model here but I hope you can understand my working.

5/8 of his salary left --- there is a total of 8 units for his salary
after he bought the refrigerator $1450
1/6 of remaining salary on digital camera, so left 5/6 of remaining salary
5/6 of remaining salary is equal to 5/8 of salary
so that means he spend 1/8 of salary on digital
so 2/8 of salary ---- $1450
1/8 of salary ----$1450/2 = $725
Muthu's salary ---- $725 x 8 = $5800