Tutor MathsGuru: Ask me for your burning Maths questions!

[Dharma]

KSP:

I need help on the 2 questions below.


1. The figure below is not drawn to scale. Given that the area of WXYZ is 40cm sq, find the area of the shaded part. Ans: 68cm sq

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

The shaded area consist of 2 triangles with height of 18cm and total base length of 12cm but the have an overlapping area of 40cm2 (i.e. Area of WXYZ)
Shaded area = (½ x 18 x 12)cm2 – Area of WXYZ = 108cm2 – 40cm2 = 68cm2

[Dharma]

KSP:

I need help on the 2 questions below.



2. The figure below is made up of two identical right-angled triangles, a small square and a big square. The parimeter of the shaded region is 50cm, and the total area of the two unshaded squares is 254.5cm sq. Find the total area of the two shaded right-angled triangles. Ans: 114.75cm sq

http://www.postimage.org/image.php?v=gxNVMm9

Side of large square = 1u
Side of small square = 1p

1u + 1p = (50 – 6)/ 2 = 22

Slide up the triangle with the larger square up the slope and u get 2 squares and a rectangle.

Shaded area = [(1u + 1p) x (1u + 1p) – 254.5] / 2 = [(22 x22) – 254.5] /2 = 114.75

[Dharma]

KSP:

How do you get 84?

84 is the smallest number that is divisible by 4,6 and 7

[KSP]

Dharma:

84 is the smallest number that is divisible by 4,6 and 7

Thanks for all your help.

[mathsguru]

YLH88:

Hi Mathsguru,


Need your help with the below question :

Dan and Mark received some money from their father.
Mark would have $128 more than Dan if Dan gave 2/5 of his share to Mark.
Mark would have $288 more than Dan if Dan gave 2/3 of his share to Mark.
How much money did Dan receive from his father ?

Thank you so much!

Hi YLH88,

Here's my solution. Apologies for the delayed reply.


MathsGuru

http://www.postimage.org/image.php?v=Pqys7r0

[YLH88]

Hi Mathsguru,


Thank you so much for the solution!! There’s no need to apologies

Regards

[mathsguru]

firebird:

Dear mathsguru


Please help me on the following P6 maths

1a) The long staircase at an HDB block has 300 steps. Micheal climed 3 steps at one go while his brother, Terry climbed 4 steps. If the steps both of them stepped on is counted once only, how many steps on the long staircase did they step on?

1b) The long staircase at an HDB block has 300 steps. Micheal climed 3 steps at one go while his brother, Terry climbed 4 steps. How many steps on the long staircase did they step on?


2) Gibson had 50-dollar, 20-dollar and 10-dollar tickets for a school funfair in the ratio of 1:5:4. The total value of the funfair tickets was $3,420.

a) Find the number of each type of tickets he had.

I manged to get as the given answer 50-dollar: 18, 20-dollar: 90 and 10-dollar : 72

b) After selling 1/4 of the 10-dollar tickets and a few 20-dollar tickets, he found that 2/11 of the remaining tickets were 50-dollar tickets. How many 20-dollar tickets did he sell?

For 2b I got 27 but the given answer is 17. Were did I go wrong?

3) A marathon runner has some water in his water bottle. Every time he comes to a refill station, he doubles the amount of water in his bottle.
Every time he comes to a rest stop, he drinks 500ml of his water.
During one race, the marathon runner passes a refill station and a rest stop three times. After the third rest stop, he finds his water bottle empty.

How much water did he have in the bottle at the begining of the race?

Many thanks
Firebird

Hi Firebird,

1a) For this question, we have to look at the LCM of 3 & 4 which is 12. This means that they will step on the same step every 12th step.

Taking 300/12=25. However, we have to add the very 1st step which both of them started on. Hence, they stepped on 26 steps.

1b) Steps Michael stepped on = 300 / 3 = 100
Steps Terry stepped on = 300 / 4 = 75
We have to subtract away the double-counted steps (stepped by both of them) which is 25 (note that the 1st step is not counted since they \"skipped\" it; both of them climbed 3 or 4 steps at one go).
Hence, answer = 100 + 75 - 25 = 150.

2a) We should convert the quantity ratio to \"value\" ratio:
1 x 50 : 5 x 20 : 4 x 10 = 50 : 100 : 40.
Therefore, 190 units = $3420. 1 unit = $18. The ratio is hence 900 : 1800 : 720.

No. of $50-tickets = $900 / $50 = 18.
No. of $20-tickets = $1800 / $20 = 90.
No. of $10-tickets = $720 / $10 = 72.

2b) There were 18 $50-tickets. If 2/11 is 18, then 9/11 = 18 / 2 x 9 = 81.

Since he sold 1/4 of the $10-tickets, there were 3/4 x 72 = 54 $10-tickets left. 81 - 54 = 27 $20-tickets left.

Number of $20-tickets sold = 90 - 27 = 63.


As for Question 3, I'll post my solution later on. Gotta rush off now.

Regards,
MathsGuru

[freakmum]

Mathsguru, how to solve this question?

If alan gives ben 6 sweets, the ratio of the number of sweets Alan will have to the number of sweets Ben will have is 2:5.
If Ben gives alan 8 sweets, the ratio of the number of sweets alan will have to the number of sweets ben will have is 1:2.
How many sweets did alan have at first?

[KSP]

Hi mathsguru, I have the working for these 2 questions from Dharma but can you show me the model method to solve them? Thanks.


1. Container A contains 250 red marbles and 200 blue marbles. Container B contains 600 red marbles and 150 blue marbles. How many red and blue marbles must be moved from Container A to Container B such that 25% of the marbles in Container A are red and 75% of the marbles in Container B are red? Ans: 350


2. In a math competition, participants can obtain 4 possible award: Gold, Silver, Bronze and Participation. 3/7 of the participants obtained Gold awards, 1/4 of the them obtained Silver awards, and 1/6 of them obtained Bronze awards. Given that there were less than 100 participants taking the competition,
a) How many participants obtained the awards for Participation? Ans: 13
b) How many more participants obtained Gold awards then Bronze awards? Ans: 22

[starlight1968sg]

Hi folks,

I need some help on p5 questions:

1) A greengrocer had 75 more apples than oranges at first. After selling 4/5 of the apples and 3/4 of the oranges, he had 285 fruits left.
(a) How many apples did he sell?
(b) What fraction of the fruits sold were oranges?
(ans: 540;5/11)

2) Ben and Caleb read a total of 60 books in November. In December, Ben read 15 fewer books than Caleb who read thrice as many books as he did in November. If both of them read a total of 90 books in December, how many books did Ben read in Nov and Dec?
(ans: 78 books)

MTIA.