Tutor MathsGuru: Ask me for your burning Maths questions!

[Dharma]

YLH88:

hi Mathsguru,


Need help in solving the following questions :


3) Celia wants to make as much tropical fruit shake as possible. The tropical fruit shake comprises of honey, strawberry and milk in the ratio of 1 : 3 : 7. She found that honey is sold at $1.50 per 100g, strawberry at $2 per 100g and milk at $1 per 100g. If she already has 900g of honey and $161 to spend,
a) find the amount of honey, strawberry and milk she can buy to maximize the amount of tropical fruit shake she can make.
b) How much money would she have left after buying honey, strawberry and milk ?


Thank you very much!

Honey : 1u
Strawberry : 3u
Milk : 7u

Honey : $1.50/100g
Strawberry : $2.00/100g
Milk : $1.00/100g

Since Celia already has 900g of honey; she needs to spend on strawberry and milk in terms of qty in ratio of 1: 3 : 7
2700g x $2/100g of strawberry = $54
6300g x $1/100g of milk = $63

$54 + 63 = $117
$161 - $ 117 = $44 (amt left)

1u($1.50) + 3u($2.00) + 7u($1.00) < $44
$14.5u < $44
1u = 3

a)\tAmt of honey = 300g
Amt of strawberry = 2700g + 900g = 3600g
Amt of milk = 6300g + 2100g = 8400g


b) Amt of money spent
= $54 + 63 + 300($1.50/100g) + 900g ($2.00/100g) + 2100g ($1.00/100g)
= $54 + 63 + $4.50 + $18 + $21
= $160.50

Amt of money left = $161.00 - $160.50 = $0.50

[abc_parent]

Hi to all gurus,


I need help!

Q1) Rectangle ABCD is divided into 9 small identical rectangules as shown. The perimeter of rectangle ABCD is 92cm. Find the area of 1 small rectangle.

Answer: 56 cm(square) - how to get to answer? I cannot upload image. if somebody can help, please pm me !! thanks!!!

Q2) 1 + 2+ 3 + 4 + … + 94 + 96 + 96 + 97
When the first 97 whole numbers are added up, what is the digit in the ones place of this total?

Answer: 4753 (is there a shortcut to do this question?)

Q3) A set of dictionaries which fitted exactly 4 shelves, each 2.05m long, was replaced by a new set. Every 7 old dictionaries was replaced by 4 new ones, each 5 cm thick. If the new set of dictionaries also fitted the 4 shelves exactly, what was the difference in the number of books between the two sets?

Answer: 120 dictionaries

[Vanilla Cake]

abc_parent:

Hi to all gurus,

I need help!

Hi abc_parent,
I am not a guru but a typical Sec 2 girl. My younger sister will be taking PSLE Maths in 2011 and I am helping out so that my younger sister can learn different techniques to solve different Maths problem sums from different helpful readers in this forum.

You need to learn how to upload image in this forum otherwise your posted question will be incomplete for readers to solve them. Hope that Chief and moderators can refer you to the link to upload images in this forum.:D

abc_parent:

Q1) Rectangle ABCD is divided into 9 small identical rectangules as shown. The perimeter of rectangle ABCD is 92cm. Find the area of 1 small rectangle.

Answer: 56 cm(square) - how to get to answer? I cannot upload image. if somebody can help, please pm me !! thanks!!!

Pls refer to this http://www.onsponge.com/forum/35-thinkingmathonsponge/2763-p6-maths.html for the clear and helpful solution by Tracey Lim.

abc_parent:

Q2) 1 + 2+ 3 + 4 + .... + 94 + 96 + 96 + 97
When the first 97 whole numbers are added up, what is the digit in the ones place of this total?

Answer: 4753 (is there a shortcut to do this question?)

(1+97)/2x97 = 4753
The digit in the ones place of this total is 3.

abc_parent:

Q3) A set of dictionaries which fitted exactly 4 shelves, each 2.05m long, was replaced by a new set. Every 7 old dictionaries was replaced by 4 new ones, each 5 cm thick. If the new set of dictionaries also fitted the 4 shelves exactly, what was the difference in the number of books between the two sets?
Answer: 120 dictionaries

Pls refer to this http://www.onsponge.com/forum/35-thinkingmathonsponge/2485-p6-maths.html for the solution.

[Maths Monster]

delete

[Yerdua]

Hi,

These are p1 qns under the "Addition and Subtraction Within 20" topic.
Qns 1: ___ +8-5= 10
Qns 2: ____-7+4=10

Pls advise on how should i teach my ds? Thks thks!

[YLH88]

Hi Vanilla Cake, Dharma,


Thank you so much!!

[MathemathicsPenguin]

sorry, careless..... :oops:

[Vanilla Cake]

MathemathicsPenguin:

Maths Monster:

Can anyone solve this with model?


Given,
p : s = 2 : 5
p : (q + r) = 1 : 3
r : (q + s) = 1 : 2

what is p : q : r : s?

Hi Maths Monster,

Here is the steps and attached model

P:S:Q+R=2:5:6
S+Q:R=1:2
5+6=11
1+2=3
Cross-multiply 11 and 3
S+Q:R=22:11, S:Q+R=15:18
15-11 or 22-18 =4. Q=4.2X3=6=P.
P:Q:R:S = 6:4:11:18.

http://www.postimage.org/image.php?v=aVtHC40

Hi Maths Monster,
Interesting question. Is ratio acceptable to solve instead of model and can I get at least half of the allocated marks for this question? Let's wait patiently for Mathsguru's model solution.


Case 1
p : s
2 : 5

Case 2
p : (q+r)
1 : 3

Case 3
r : (q+s)
1 : 2

Expand case 2 by multiplying by 2 so that \"p\" in case 2 is equivalent to \"p\" in case 1
Expanded Case 2
p : (q+r)
2 : 6

Now, add \"s\" in case 1 and \"(q+r)\" in expanded case 2-> 5+6 = 11.
Note that in case 3, \"r+(q+s)\" = 1+2 = 3.
LCM of 3 and 11 = 33
Since \"s\" in case 1 is 5 and \"(q+r)\" in expanded case 2 is 6, add 5+6= 11.So multiply case 1 and expanded case 2 by 3 to make them equivalent.(11x3=33)
Finally expand case 3 by multiply by 11 so that the new ratio will be added to 33.

Expanded Case 1
p : s
6 : 15

Final Expanded Case 2
p : (q+r)
6 : 18

Expanded Case 3
r : (q+s)
11 : 22

p = 6
r = 11
q = 18-11 = 7
s = 22-7 = 15

p : q : r : s is 6 : 7 : 11 : 15

[Dharma]

Maths Monster:

Can anyone solve this with model?


Given,
p : s = 2 : 5
p : (q + r) = 1 : 3
r : (q + s) = 1 : 2

what is p : q : r : s?

Hi Maths Monster,

This ratio question can be solved easily using ratios as shown by Vanilla Cake. Model method is not required as the qn actually wants you to express the 4 unknowns in one ratio. The qn gives info on 3 diiferent ratios involving 2 or 3 unknowns.

p : s : (q + r) = 2 : 5 : 6
p : (q + r + s )= 2 : 11
r : (q + s) = 1 : 2; so r : (q +r + s) = 1:3
So,
p : (q + r + s) = 6: 33
p : (q + s) : r = 6 : 22 : 11
p : s = 2 : 5 = 6 : 15
p : (q + s) = 6 : (q + 15)

When p = 6; q = 22- 15 = 7; r = 11; s = 15
p:q:r:s = 6:7:11:15

[Dharma]

Yerdua:

Hi,

These are p1 qns under the \"Addition and Subtraction Within 20\" topic.
Qns 1: ___ +8-5= 10
Qns 2: ____-7+4=10

Pls advise on how should i teach my ds? Thks thks!

For this sort of qns, best to work backwards.

For Qn 1

Let’s say we Ali has a certain number of sweets at first. His mother gives him 8 sweets and then he gives 5 sweets to his sister. Ali will have 10 sweets at last.

Now working backwards, Ali would have had 15 sweets (10 + 5) i.e. 5 sweets more, before giving away 5 sweets to his sister.

Before that, Ali will be receive 8 sweets from his mum to have 15 sweets. So, before getting the 8 sweets from his mum, Ali will have 8 sweets less ( 15 – 8= 7) Ali will have 7 sweets at first.

No. of sweets at first = 10 + 5 - 8 = 7

You may wish to try Qn 2.