Tutor MathsGuru: Ask me for your burning Maths questions!

[Vanilla Cake]

YLH88:

Hi Vanilla Cake,


Thank you !

Hi YLH88,
You are welcome. My younger sister is also interested to learn the model solution for this problem. While waiting for Mathsguru's model solution, let's use algebra to get the answer.

YLH88:

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 ?

Case 1
3/5D+128 = M + 2/5D
1/5D+128 = M

Case 2
1/3D+288 = M + 2/3D
288 = M + 1/3D
288-1/3D = M

1/5D+128=288-1/3D
8/15D=160
D = 300

Amount of money that Dan received from his father was $300

[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

[starlight1968sg]

YLH88:

Hi Mathsguru,


Need your help with the below questions :

1) Doran had 8/11 of the number of game cards Thomas had. After Thomas lost 18 cards to Doran, they both had the same number of cards.

a) How many more game cards did Thomas have than Doran at first ?
b) As the game continued, Doran won more cards from Thomas. How many more cards did Thomas lose to Doran such that Doran has 3 times as many cards as him ?

I'm able to get the answer for (a), which is 36. But can't find for (b)

Thank you!

Regarding the above question:
(a) No problem in getting 36 cards. This means orginally Doran has 96 cards and Thomas has 132 cards. (checked: 96/132 = 8/11)

For b: since the question mentioned \"As the game continued...\", is it safe to assume that both have the same number of cards to start with as this point?

Thanks.

[Vanilla Cake]

Hi firebird,

Let me offer a little help while waiting for detailed solutions from Mathsguru. Hope it maybe of some use for you.

firebird:

1) The long staircase at an HDB block has 300 steps. Micheal climbed 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?

Answer
LCM of 3 and 4 is 12
Step numbers : 12, 24, 36, 48...... are stepped by both brothers, so it's counted as once.

300÷12=25
300÷3=100
300÷4=75
100+75-25=150

Number of steps on the long staircase stepped by them was 150

firebird:

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.
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?

Answer
(a)
1 \"set\" = $(50x1 + 20x5 + 10x4) = $190
$(3420÷190) = 18

18x1 =18
18x5=90
18x4 = 72

Number of each type of tickets he had was as follows:
50-dollar: 18
20-dollar: 90
10-dollar: 72

(b)
1/4x72=18
2/11->18
9/11->81
72-18=54
Number of 20-dollar tickets unsold was 81-54=27
90-27=63
Number of 20-dollar tickets sold by Gibson was 63

firebird:

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 beginning of the race?

Answer
Work backwards from empty water bottle after the third rest stop to the beginning of the race:

Third rest stop-> Empty, 500, 250
Before -> 250, 750, 375
Beginning-> 375, 875, 437.5

Amount of water that the marathon runner had in the bottle at the beginning of the race was 437.5 ml

Pls refer to these links for good explanations for the last 2 questions:
http://www.onsponge.com/forum/35-thinkingmathonsponge/1837-p6-maths-2009-pei-hwa-presbyterian-pri-sch-sa1.html
http://psle2010a.blogspot.com/2010/03/peihwa.html
http://psle2010a.blogspot.com/2010/03/marathon-runner-has-some-water-in-his.html
From your post @ 28 Mar 2010, 02:46 am, you are hardworking and will score well in your PSLE Maths. Good luck.

[CoffeeCat]

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

1a) I believe this question is asking for the lowest common multiples of 3 and 4. The working is ... lcm of 3 and 4 = 12
300 / 12 = 25

1b)no. of steps Michael stepped on = 300/3 = 100
no. of steps terry stepped on = 300/4 = 75
total = 175

[firebird]

Dear Vanilla Cake


Good afternoon.

Many thanks.

Your explaination is very clear. Perhaps CoffeeCat could take a look.

With best regards.
firebird

[CoffeeCat]

Oops lol my mistake I read the question wrongly.

[YLH88]

[quote]
Case 1
3/5D+128 = M + 2/5D
1/5D+128 = M

Case 2
1/3D+288 = M + 2/3D
288 = M + 1/3D
288-1/3D = M

1/5D+128=288-1/3D
8/15D=160
D = 300

Amount of money that Dan received from his father was $300[/quote]Hi Vanilla Cake,

Thank you for the solution !

[help]

Please help to solve the problem using model


In a bag, there are red, yellow and blue marbles. There were twice as many red marbles as yellow marbles and twice as many yellow marbles as blue marbles at first. After removing 15 blue marbles and some yellow marbles from the bag, the number of red marbles became thrice that of the yellow marbles but the number of yellow marbles was still twice that of the blue marbles. What was the total number of marbles in the bag at first?[/size]

[KSP]

Hi Mathsguru and everyone,


I came across this maths book Unit Transfer Method - Mastering Heuristic Series by Sunny Tan, Price S$37.50 which I find it very helpfut and easy to understand. Have you seen this book before and what is your comment? Thanks.