Tutor MathsGuru: Ask me for your burning Maths questions!

[iFruit]

Daddy:

Hi,


Another Question to ask..Thanks

1. Evaluate the following series:
(2010-2009+2008) + (2007-2006+2005) +...+(1020-1019+1018).

:? What question is this? :!:
Thanks

Need to know a couple of formulas for this type of problems..

Each term in bracket reduces to (smallest number +1), with difference in terms being three...so the sequence is like

1019, 1022, 1025.....2009 (from right to left) with a common diff of 3

So number of terms = (last term - first term)/diff + 1 = (2009 - 1019)/3 + 1 = 331

Sum of terms = (last term + first term)(num of terms)/2 = (1019 + 2009)x331/2 = 3028 x 331/2 = 1514 x 331 = 501134

[kancheongmum]

x6michelle9x:

Hi, I would appreciate if someone can help to solve this problem without using algebra, thanks in advance!


The average cost of a few books was $8. After a book which costs $32 was added, the average cost becomes $12. How many books are there now?

Hi x6michelle9x

$32 - $12 = $20 (we have to minus out the book that was added)

$20 is the amount that contribute to the increased of the average cost of a few books

$12 - $8 = $4

$20/$4 = 5 books

No. of books now --- 5+1 = 6 books (answer)

Check:
$8 x 5 = $40
$40+$32 = $72
$72/6 = $12

[x6michelle9x]

kancheongmum:

x6michelle9x:

Hi, I would appreciate if someone can help to solve this problem without using algebra, thanks in advance!


The average cost of a few books was $8. After a book which costs $32 was added, the average cost becomes $12. How many books are there now?

Hi x6michelle9x

$32 - $12 = $20 (we have to minus out the book that was added)

$20 is the amount that contribute to the increased of the average cost of a few books

$12 - $8 = $4

$20/$4 = 5 books

No. of books now --- 5+1 = 6 books (answer)

Check:
$8 x 5 = $40
$40+$32 = $72
$72/6 = $12

Hi, thanks for the prompt reply
However, I can't figure out the rationale behind '$32 - $12 = $20'. Why does $32-$12 equals to 'minus out the book that was added'. Could you help me with this? Thanks a lot!

[CTong]

1) Ali, Bala Clyde and Dingyi shared a box of pens. Ali received 20% of the total number of pends which Bala, Clyde and Dingyi received altogether. Bala received 50% of the total number of pens which Ali, Clyde and Dinyi received altogether. Clyde received 80% of the total number of pens which Ali, Bala and Dinyi received altogether. Dingyi received 6 pens. How many pens were in the box at first?


2) Mrs Raju bought 20 bottles of milk and 5 boxes of cornflakes from the supermarket. If she had bought these items at 20% discount, the amount of money she saved could buy another 3 more boxes of cornflakes at the usual price. The usual price of a bottle of milk was $2.15. What was the usual price of a box of cornflakes?

3) Jolene and Penny had a sum of money. Jolene gave Penny 0.4 of her money. Penny ghen gave Jolene 1/2 of her money. In the end, Jolene had three times the amount of money that Penny had. If Jolene gave Penny $125 more than what Penny gave Jolene, how much money did Jolene have at first?>

[kancheongmum]

x6michelle9x:

kancheongmum:

[quote=\"x6michelle9x\"]Hi, I would appreciate if someone can help to solve this problem without using algebra, thanks in advance!


The average cost of a few books was $8. After a book which costs $32 was added, the average cost becomes $12. How many books are there now?

Hi, thanks for the prompt reply
However, I can't figure out the rationale behind '$32 - $12 = $20'. Why does $32-$12 equals to 'minus out the book that was added'. Could you help me with this? Thanks a lot!

[/quote]Hi

Maybe is clearer for me to say this way:

$32 - $12 =$20

$20 is the total difference in amount over the same number of books(before one book is added)

\"minus out the book that was added\" I mean the new average amount must be subtracted from the price of the additional book.

I understand the confusion. It took me sometime to explain to my son. I draw diagrams to help him understand but sorry I don't know how to illustrate here.

Hope this helps

[pecalis]

kancheongmum:

x6michelle9x:

Hi, I would appreciate if someone can help to solve this problem without using algebra, thanks in advance!


The average cost of a few books was $8. After a book which costs $32 was added, the average cost becomes $12. How many books are there now?

Hi, thanks for the prompt reply
However, I can't figure out the rationale behind '$32 - $12 = $20'. Why does $32-$12 equals to 'minus out the book that was added'. Could you help me with this? Thanks a lot!

New price - new average = 32 - 12 = 20
The excess 20 is spread out evenly to bring the ave of the rest from 8 to 12 ie. 12 - 8 = 4 (each book increase by 4)
so 20/4=5, therefore, there are 5+1=6 books now
HTHs

[Daddy]

Hi


I have a question to ask. Thanks…

1. The number of boys to the number of girls attending Tuition class A and Tuition class B are 2:1 and 2:7 respectively. The ratio of the total number of pupils in Tuition class A to that of tuition class B is 2:3.
a) What is the ratio of the number of boys in Tuition class A to the number of boys in Tuition class B? Give your answer in simplest form.
b) There are 35 more girls than boys in Tuition class B. For both tuition classes, each cild has to pay $280 every month. How much fess does both tuition classes collect in all for 12 months?

Thanks
Daddy

[Muffins]

hi Daddy, are you sure that you have written the question correctly? Because, If the total number of B + G for Tuition A is 2 + 1 = 3, and for B, 2 + 7 = 9, the ration would be 3 : 9 = 1 : 3, not 2 : 3…


Thanks…

[Mathmaniac]

Daddy:

Hi


I have a question to ask. Thanks..

1. The number of boys to the number of girls attending Tuition class A and Tuition class B are 2:1 and 2:7 respectively. The ratio of the total number of pupils in Tuition class A to that of tuition class B is 2:3.
a) What is the ratio of the number of boys in Tuition class A to the number of boys in Tuition class B? Give your answer in simplest form.
b) There are 35 more girls than boys in Tuition class B. For both tuition classes, each cild has to pay $280 every month. How much fess does both tuition classes collect in all for 12 months?

Thanks
Daddy

a) (2/3 x 2) : (2/9 x 3) = (12/9) : (6/9) = 12:6 = 2:1

b) (7/9 - 2/9) of class B = 35
5/9 of class B = 35
class B = 35 x 9/5 = 63
class A = 63 x 2/3 = 42
total = 63+42 = 105
fees = 105 x $280

[Muffins]

O… I get it… Thanks MathManiac!!!