Tutor MathsGuru: Ask me for your burning Maths questions!

[pandan]

Hi all,


My problem is somehow solved after I rebooted my pc. thank you.

[Tang]

sachiko:

2. A highlighter costs 3 times as much as a marker. Bert spent 2/5 of his money on markers and 1/3 of the remainder on a pen. The highlighter cost $0.90. How many markers did he buy?


Thank you.

1 - 2/5 = 3/5

1/3 x 3/5 = 1/5

3/5 - 1/5 = 2/5

2 u --> $0.90

1 highlighter --> $0.90

1 marker --> 1/3 x 0.90 = $0.30

0.90/0.30 = 3 markers

He bought 3 markers.

[firebird]

Dear mathsguru


Good morning.

Please help me on the following maths:

1) A man travels from Town X to Town Y at 4 Km/h and from Town Y to Town X at 6 Km/h via the same route. The whole journey takes 45 minutes. Find the distance from Town X to Town Y.

Given answer 1.8 Km, however my answer is 1.875 km.

2) A pen costs 40 cents more than a ruler. John paid $x for a pen and a ruler. Find the cost of a ruler in cents.

Given answer is (50-20)cents

3) A Spaceship lego set cost $80 more than a Tommy train set at a toyshop. During its anniversar, a storewide 20% discount was given to all customers. In addition, members of the toyshop enjoy an addtional 10% discount. Mr. Tan, a member of the toyshop, paid a total of $345.60 for the Spaceship lego set and the Tommy train set. Calculate the original price of the Spaceship set.

Given answer is $28

4) Mr. Tan took 6 hours to drive from Town A to Town B.
Mr. Lim, who started at the same time as Mr. Tan, took 4 hours to drive from Town B to Town A. When they meet each other, they were 48 km from the midpoint of Town A and Town B.
(a) Calculate the distance between Town A and Town B.
(b) Calculate the speed of Mr. Tan.

5) 20% of John’s saving is $120 more than 30% of Brian’s savings. After John spent 5/6 of his savings and Brian spent 1/2 of his savings, John has $20 more than Brian. Find the saving of John at first.

Many thanks
firebird

[Vanilla Cake]

Hi firebird,

All your 5 questions are taken from Catholic High School 2009 Primary 6 Preliminary Examination 3 Maths set on 26 August 2009.

firebird:

1) A man travels from Town X to Town Y at 4 Km/h and from Town Y to Town X at 6 Km/h via the same route. The whole journey takes 45 minutes. Find the distance from Town X to Town Y.

This is a 2-mark question from Q30 - paper 1.
Concept - For constant/fixed/same distance, speed is inversely proportional to time.

Ratio of speed
4 : 6

Ratio of time
6 : 4

Total time = 45 min = 0.75 h
(6+4)units = 10 units
10 units = 0.75 h
1 unit = 0.075 h

Time taken for the man to travel from Town X to Town Y at 4 km/h = 6 units x 0.075 h = 0.45 h
Distance from Town X to Town Y = 0.45 h x 4 km/h = 1.8 km

firebird:

2) A pen costs 40 cents more than a ruler. John paid $x for a pen and a ruler. Find the cost of a ruler in cents.

This is a 2-mark question from Q1 - paper 2.
$x = 100x cents
Ruler -> u
Pen -> u + 40 cents
Total cost of a pen and a ruler = 100x cents
Cost of a ruler = (100x-40)cents÷2 = (50x-20) cents

firebird:

3) A Spaceship lego set cost $80 more than a Tommy train set at a toyshop. During its anniversar, a storewide 20% discount was given to all customers. In addition, members of the toyshop enjoy an addtional 10% discount. Mr. Tan, a member of the toyshop, paid a total of $345.60 for the Spaceship lego set and the Tommy train set. Calculate the original price of the Spaceship set.

This is a 5-mark question from Q16 - paper 2.
Spaceship Lego Set -> SL
Tommy train -> TT

SL = 100%+$80
TT = 100%

For members only:
SL = [80/100x(100%+80)]x90/100
= (80%+64)x90/100
= 72% + $57.60

TT = (80/100x100%)x90/100
= 72%

72%+72%+$57.60 = $345.60
144% = $288
1% = $2

100% = $200
$(200+80) = $280

Original price of the Spaceship Lego set was $280

[Vanilla Cake]

firebird:

4) Mr. Tan took 6 hours to drive from Town A to Town B.

Mr. Lim, who started at the same time as Mr. Tan, took 4 hours to drive from Town B to Town A. When they meet each other, they were 48 km from the midpoint of Town A and Town B.
(a) Calculate the distance between Town A and Town B.
(b) Calculate the speed of Mr. Tan.

This is a 5-mark question from Q17 - paper 2 from Catholic High School 2009 P6 Prelim Exam 3 set on 26 August 2009.

Ratio of time
Mr Tan : Mr Lim
6 : 4

Ratio of distance
Mr Tan : Mr Lim
4 : 6

Distance from Town A to midpoint for Mr Tan -> 4 units + 48 km
which was the same as distance from midpoint to Town B for him.
At the point where both met @ 48 km away from midpoint, Mr Lim had travelled 6 units.

6 units = 48km + 48km + 4 units
2 units = 96 km
1 unit = 48 km

Total distance = (4+6) units = 10 units
10 units = 48x10 = 480 km

(a) Distance between Town A and Town B was 480 km

(b) Speed of Mr Tan = 480 km÷6 hours = 80 km/h

Pls refer to this http://prischoolmaths.blogspot.com/2009/06/maths-speed_4616.html for clear understanding which has the same concept. This is ACS(J)/ACS(P)2008 P6 Prelim Q43.

[Vanilla Cake]

firebird:

5) 20% of John's saving is $120 more than 30% of Brian's savings. After John spent 5/6 of his savings and Brian spent 1/2 of his savings, John has $20 more than Brian. Find the saving of John at first.

This is a 5-mark question from Q18 - paper 2 from Catholic High School 2009 P6 Prelim Exam 3 set on 26 August 2009.


John -> John
Brian -> B

20% = 1/5
1/5J =3/10B+120
J = 1 and 5/10B + 600

Before
J = 1.5 unit + 600
B = unit

After
J = 0.25 unit + 100
B = 0.5 unit

0.25 unit + 100 = 0.5 unit + 20
0.25 unit = 80
1 unit = $320

1.5 units = $ 480
$(480+600) = $1080

At first, savings of John was $1080

Sorry for the messy solution, hope that Mathsguru will come up a model solution to help you understand better.
Thanks.

[mathsguru]

starlight1968sg:

Hi,

I need some help again.

1) Andy, Betty, Candy and Danny each have some money. The amount of money Andy has is 1/3 of the total amount of money Betty, Candy and Danny have. The amount of money Betty has is 1/4 of the total amount of money Andy, Candy and Danny have. The amount of money Candy has is 1/5 of the total amount of money Andy, Betty and Danny have. If Danny has $1725, how much do they have altogether?

2) Tom and Jerry each has some money. If Tom spends $90 per day and Jerry spends $45 per day, Tom will have $1100 left when Jerry has spent all his money. If Tom spends $45 each day and Jerry spends $90 each day, Tom will have $1700 left when Jerry has spent all his money. How much did Jerry have?

I am totally clueless on how to start?

MTIA.

Hi Starlight1968sg,

Sorry for the delay! Have been quite tied up this week.

Here're my solutions.

Cheers,
MathsGuru

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

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

[mathsguru]

ChiefKiasu:

mathsguru, just as a small token of our appreciation for the help you have rendered to our community, we award you 5000 KPs for you kind contributions!

Hi ChiefKiasu,

Thank you thank you!!

Wow...that's really a pleasant surprise *flattered*...although I must confess I'm clueless how to use the KPs...hehe...will go read up on that!

Really glad to know that my efforts have been constructive so far!! Will continue to gambatte!!

Cheers,
MathsGuru

[mathsguru]

Tiramisu Coco:

Hi mathsguru,


Need your help to solve this problem sum:

Roger had $186 more than Belinda. When he gave $20 to Belinda he still had three times as much money as she. How much did Roger have at first?

Thanks.

Hi Tiramisu Coco,

Here's my solution!


MathsGuru

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

[mathsguru]

chanpy:

Tagged as challenging question for P2 -


Mary baked 34 cupcakes for her friends. She packed 4 cupcakes into each bag. What is the greatest number of bags she needed to pack all the cupcakes?

What would be your answer - 8 or 9 bags?

The answer given by the teacher is 8 bags.

Appreciate advice on how to explain to kid.

TIA

Hi Chanpy,

The answer should be 9 bags, because 34 / 4 = 8 R2 and since she needs to pack ALL the cupcakes, it will have to be 8 + 1 = 9 bags.

I'm rather concerned why the teacher gave 8 bags as the answer. I seriously hope it is a typo error by the teacher, else it is really worrying...

:?
MathsGuru