Tutor MathsGuru: Ask me for your burning Maths questions!

[adhdadhd]

1) Sally and Joseph have an equal number of coins in their coin boxes. Every day, Sally takes out 5 coins and Joseph takes out 3 coins. When Sally finishes all her coins, Joseph still has 64 coins left. How many coins do they have altogether at first ?


Using guess and check method…
S [5] -----[5]
J [3] ---- [3][64]

S\tJ\tDiff
35\t21\t14
85\t51\t34
135\t81\t54
160\t96\t64


They have 320 coins at first.

(check: 32x5 = 160. 32 x 3= 96, 160-96=64).

Algebra can be used too…

[Vanilla Cake]

YLH88:

1) Sally and Joseph have an equal number of coins in their coin boxes. Every day, Sally takes out 5 coins and Joseph takes out 3 coins. When Sally finishes all her coins, Joseph still has 64 coins left. How many coins do they have altogether at first ?

Difference in the daily spending of coins = 5-3 = 2
Difference in the leftover of coins = 64
64÷2 = 32 (Number of days)

Number of coins that Sally had = 5x32= 160
160x2 = 320
At first, they have 320 coins.

YLH88:

2) At 2pm, a car travelled from Town A to Town B at an average speed of 80 km/h. At the same tme, a van travelled from Town B to Town A. After sometime, the car and van passed each other and were 20 km apart at 5pm. The car arrived at Town B at 7pm
a) Find the average speed of the van
b) What time did the van arrive at Town B ?

From 5 pm to 7 pm, the car travelled 80 km/h x 2 h = 160 km
From 2 pm to 5 pm. distance travelled by the van = (160+20) km = 180 km
(a) Average speed of the van = 180÷3 = 60 km/h

Time taken for the car to complete the journey from Town A to Town B = 5 hours.
Distance between Town A and Town B = 80 km/h x 5 h = 400 km
400÷60 (60 is the average speed of van)
6⅔ h = 6 h 40 min
Add 6 h 40 min to 2 pm
(b) Time for the van to arrive at Town B was 8.40 pm

YLH88:

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 ?

Hi YLH88,
I am not so sure about the highlighted statement in red colour in this question.So, pls pardon me if my working is incorrect . Hope that Mathsguru and other members such as Dharma etc will forward the correct solution. Thanks.

H : S : M
1 : 3 : 7
100 : 300 : 700
Total = 100+300+700 = 1100g

H: 1 x $1.50 = $1.50
S: 3 x $2 = $6.00
M: 7 x $1 = $7.00

1 set = $(1.50+6.00+7.00) = $14.50
161÷14.5 = 11 R $1.50

11x1100g = 12100g = 12.1 kg
(a) Maximum amount of tropical fruit shake that can be made = 12.1 kg

(b) Money left after buying honey, strawberry and milk is $1.50

[Dharma]

ruyu:

Dharma:

[quote=\"ruyu\"]Suzy bought 12 stickers from Singapura Bookshop. The price of each sticker was the same. If the price of 1 sticker was cheaper by 5-cents, she could have bought4 more stickers at the cheaper price. How much did she spend on 12 stickers?

Cost of 12 stickers = 12(1u)

12(1u) = 11(1u) + 5(1u - 5 cents)
4u = 25 cents
1u = 6.25 cents

12 stickers cost = 12 x 6.25 cents = 75 cents

dont understand :?[/quote]Sorry ruyu,

Actually, I misunderstood the qn.

I assumed that Suzy only bought 1 sticker at 5cents cheaper and the other 11 stickers were bought at the original price and by doing that, she managed to buy 4 more stickers at the cheaper price.

It should have been more like Suzy buying 16 stickers (12 + 4) at a cheaper price i.e 5cents less than the original price. Then the cost of 12 stickers will be 240 cents as shown by Maths Monster.

[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: