Tutor MathsGuru: Ask me for your burning Maths questions!

[maths6a]

Dear Gurus out there, need help with 2 questions:-


1. If Andy runs up 7 steps of the escalator, he will take 36 sec to reach the top of the escalator. If he runs up 13 steps, he will take him only 27 sec to reach the top. How many seconds would it take him to reach the top if he did not run up any steps of the escalator at all?

2. When asked how many gold coins a miser had, his reply was, " If I divide the coins into 2 unequal numbers, then 49 times the difference between the two numbers equals the difference between the squares of the two numbers."
How many coins did he have?

Thank you in advance fof the solution.

[tianzhu]

Hi maths6a


Just curious, where are your two questions from? They don’t look like questions from past years papers.
[quote]If Andy runs up 7 steps of the escalator, he will take 36 sec to reach the top of the escalator. If he runs up 13 steps, he will take him only 27 sec to reach the top. How many seconds would it take him to reach the top if he did not run up any steps of the escalator at all? [/quote]If Andy runs up 7 steps, he needs 36 seconds to reach the top of the escalator.

If he runs up 13 steps, he needs 27 seconds to reach the top the escalator .

36-27 ----- 9
Therefore each additional step takes 9/6 -------1.5 seconds

Total steps in escalator = 7 + 36 /1.5 ----- 31

or 13 + 27/1.5 ------ 31

If he did not run up any steps, he will take 31*1.5 ------ 46.5 seconds.
[quote]When asked how many gold coins a miser had, his reply was, \" If I divide the coins into 2 unequal numbers, then 49 times the difference between the two numbers equals the difference between the squares of the two numbers.\"
How many coins did he have? [/quote]The second question involves difference of squares formula.

a2 - b2 = (a + b) (a - b) (a2 means a to the power of 2)

Given a2 - b2 = 49(a-b)

Therefore (a+b) (a-b) = 49(a-b)
Hence (a+b) =49

Use listing or GC
Try a=25, b=24
625-576 = 49(25-24)

There are 49 coins

[maths6a]

tianzhu:

Hi maths6a


Just curious, where are your two questions from? They don’t look like questions from past years papers.
[quote]If Andy runs up 7 steps of the escalator, he will take 36 sec to reach the top of the escalator. If he runs up 13 steps, he will take him only 27 sec to reach the top. How many seconds would it take him to reach the top if he did not run up any steps of the escalator at all?

If Andy runs up 7 steps, he needs 36 seconds to reach the top of the escalator.

If he runs up 13 steps, he needs 27 seconds to reach the top the escalator .

36-27 ----- 9
Therefore each additional step takes 9/6 -------1.5 seconds

Total steps in escalator = 7 + 36 /1.5 ----- 31

or 13 + 27/1.5 ------ 31

If he did not run up any steps, he will take 31*1.5 ------ 46.5 seconds.
[quote]When asked how many gold coins a miser had, his reply was, \" If I divide the coins into 2 unequal numbers, then 49 times the difference between the two numbers equals the difference between the squares of the two numbers.\"
How many coins did he have? [/quote]The second question involves difference of squares formula.

a2 - b2 = (a + b) (a - b) (a2 means a to the power of 2)

Given a2 - b2 = 49(a-b)

Therefore (a+b) (a-b) = 49(a-b)
Hence (a+b) =49

Use listing or GC
Try a=25, b=24
625-576 = 49(25-24)

There are 49 coins[/quote]Wow, what kind of questions are these? They are just 2 of the questions in my P4 neighbour's worksheet over the september holidays! Managed to help her with the rest but have no clue how to help her with these 2 so better check with the experts here. Thanks!

[Hiroii-kun]

Dear Gurus,

need help with this question.

At first, warehouse X and Y had a total of 10400 sacks of rice. After warehouse X has cleared 3/4 of its stock and warehouse Y has cleared 3/5 of its stock, warehouse Y now has 520 more sacks of rice than warehouse X. How many sacks of rice did each warehouse have at first?

Ans is 5600 & 4800 but cant seem to get it.

[Dharma]

Hiroii-kun:

Dear Gurus,

need help with this question.

At first, warehouse X and Y had a total of 10400 sacks of rice. After warehouse X has cleared 3/4 of its stock and warehouse Y has cleared 3/5 of its stock, warehouse Y now has 520 more sacks of rice than warehouse X. How many sacks of rice did each warehouse have at first?

Ans is 5600 & 4800 but cant seem to get it.

4u + 5p = 10400 ........ (1)
2p - 1u = 520 ..............(2)
8p - 4u = 2080 .............(2) x 4 = (3)

13p = 12480 ........(1) + (3)
1p = 960
1u = 1400
X => 4u = 4 x 1400 = 5600
Y => 5p = 5 x 960 = 4800

[Hiroii-kun]

Dharma:

Hiroii-kun:

Dear Gurus,

need help with this question.

At first, warehouse X and Y had a total of 10400 sacks of rice. After warehouse X has cleared 3/4 of its stock and warehouse Y has cleared 3/5 of its stock, warehouse Y now has 520 more sacks of rice than warehouse X. How many sacks of rice did each warehouse have at first?

Ans is 5600 & 4800 but cant seem to get it.

4u + 5p = 10400 ........ (1)
2p - 1u = 520 ..............(2)
8p - 4u = 2080 .............(2) x 4 = (3)

13p = 12480 ........(1) + (3)
1p = 960
1u = 1400
X => 4u = 4 x 1400 = 5600
Y => 5p = 5 x 960 = 4800

ooh thanks!

[Dharma]

maths6a:

Dear Gurus out there, need help with 2 questions:-


1. If Andy runs up 7 steps of the escalator, he will take 36 sec to reach the top of the escalator. If he runs up 13 steps, he will take him only 27 sec to reach the top. How many seconds would it take him to reach the top if he did not run up any steps of the escalator at all?

2. When asked how many gold coins a miser had, his reply was, \" If I divide the coins into 2 unequal numbers, then 49 times the difference between the two numbers equals the difference between the squares of the two numbers.\"
How many coins did he have?

Thank you in advance fof the solution.

1.\t

If Andy walks up (instead of running up) 6 more steps (13 – 7) he will take 9 secs (36s – 27s) more..
So, every 1 step that Andy walk up instead of running he will take 1.5 seconds more
Total time taken if Andy walks up all the steps = 36s + 7(1.5s) = 46.5s

2.

If the 2 numbers are A and B

49(A – B) = A^2 – B^2 (Given in Question)
(Imagine a small square of side B within a larger square of side A)
A^2 – B^2 is the difference in area between the 2 squares. (See below)

A^2 – B^2 = (A + B)(A – B)
So, A + B = 49 (Total number of coins)



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

[starlight1968sg]

Hi,

I need some help here:
Jane has 70 dresses than skirts. She sold 3/4 of the dresses and 3/5 of the skirts. She sold 126 more dresses than skirts. What fraction of the remaining clothes that Jane had were skirts?
Many thanks.

[Vanilla Cake]

starlight1968sg:

Hi,

I need some help here:
Jane has 70 dresses than skirts. She sold 3/4 of the dresses and 3/5 of the skirts. She sold 126 more dresses than skirts. What fraction of the remaining clothes that Jane had were skirts?
Many thanks.

Hi starlight1968sg,
Just curious, your question is from http://www.orlesson.org/orp/09Ma/2009-Math-SA2-SCGS.pdf.It's a 5-mark question and you changed the original name - Zara to Jane. Why?

Before
Dresses : 4u
Skirts: 4u-70

Sold
Dresses: 3u
Skirts: 3/5x(4u-70)= 2.4u-42

Sold 126 more dresses than skirts-> 3u=2.4u-42+126
0.6u=84
u = 140

After
Dresses: 1u = 140
Skirts: 4u-70-(2.4u-42) = 4u-70-2.4u+42 = 1.6u-28 = 1.6(140)-28=224-28=196

196/(140+196)=196/336 = 7/12

Fraction of the remaining clothes that Jane had were skirts = 7/12.

Hope that other members will come with model drawing solutions and other alternatives.

[firebird]

Dear maths guru


Good evening.

Please help me on the following maths which I am assisting my child:

1) Mdm Ang bought some highlighters, pens and mechanical pencils. 1/4 of them were highlighters. The number of pens she bought was 6 more than 1/2 of the total number of all items and the remaining were mechanical pencils. Each of the highlighters, pens and mechanical pencils cost $2.10, $4.05 and $1.60 respectively. She spent a total of $227.10 on all items. How many pens did she buy altogether?

This is Nanyang Primary SA 2 2009 question 18.

2) Simple sum but I want to check with you

What is the sum of all the common factors of 12, 18 and 24?

12 - 1,2,3,4,6,12 = sum of all = 28
18 - 1,2,3,6,9,18 = sum of all = 39
24 - 1,2,3,4,6,12,24 = sum of all = 60

So sum all three above = 28+39+60= 127

Kindly correct me.

Thank you.
With best regards
Firebird