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[Almighty]

Almighty:

Question :5Pattern II -photo print


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

Hi MAthmonster,Dharma,Ksi & others......
Reposting...If this qt had missed yr eye...Since i posted many qt last night.
Pl.try to help me on this too..

[Maths Monster]

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[Maths Monster]

delete

[YLH88]

Hi Maths Monster,


Thank you so much for your help!

[Tang]

Maths Monster:

Almighty:

Tom had $144 more than Ali at first. After Tom spent 25% of his money and Ali spent 1/3 of his money. Tom had $122 more than Ali. How much did Tom have at first?
Thankyou very much for all other answers too.

You're welcome.

Before:
Let u be the amount Ali has
Tom has u + 144

After:
Ali has u x 2/3
Tom has (u + 144 ) x ¾

Since Tom had $122 more than Ali, therefore:
(u + 144) x ¾ = u x 2/3 + 122
(u + 144) x 9 = u x 8 + 122 x 12
9u + 1296 = 8u + 1464
u = 168

Therefore, Ali has $168 and Tom has 168+144 = $312 at first

Check:
After
Ali has 168 x 2/3 = $112
Tom has 312 x ¾ = $234
Difference is 234 – 112 = $122

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

Note: in this question, there is no ratio, we are only given the difference. We simply give one of them as \"u\" and start to fill in the rest. To find the answer, the equation is formed in the After scenario using the $122 difference. Likewise, one can state Tom has \"u\" in before and derive the answer, should be the same.

Cheers,
MM

Tom had $144 more than Ali at first. After Tom spent 25% of his money and Ali spent 1/3 of his money. Tom had $122 more than Ali. How much did Tom have at first?


T [ 12 u ][144]
A [ 12 u ]

144 x 25% = 36

144 - 36 = $108

TN [ 9 u ][108]
AN [ 8 u]

1 u + 108 --> 122

1 u --> 122 - 108 = $14

12 u --> 14 x 12 = 168

168 + 144 = #312

Tom had $312 at first.

[Maths Monster]

delete

[Dharma]

Almighty:

Maths Monster:

[quote=\"Almighty\"]Question :8 - speed -EDITED

Tom, Bob and Kel;vin started running at the same point X at the same time round a circular track. Tom ran in a clockwise direction but Bob and Kelvin ran in an anti-clockwise direction. Tom took 7 minutes to complete each round. He met Bob after every 4 minutes and he met Kelvin after every 2 minutes. Each of them ran at the same uniform speed throughout.
a) What was the ratio of Toms speed to Kelvin's speed to Bob's speed?Ans:4:10:3.
b) When Tom and Bob met again at X after 21 minutes, Tom had already run 4200m. What was the distance ran by Kelvin when Tom met Bob at X after 21 minutes?
section B cannot understand the method.pl.brief.Ans:3500m

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

Tom ran 1 round in 7 mins. His speed is 1/7 round per min.

In 2 mins, he ran 2/7 round.
In the same time, Kelvin ran 5/7 round to meet Tom
Kelvin speed is 5/7 / 2 = 5/14 round per min.

In 4 mins, he ran 4/7 round.
In the same time, Bob ran 3/7 round to meet Tom
Bob speed is 3/7 / 4 = 3/28 round per min.

a) Ratio of speed:
Tom : Kelvin : Bob
1/7 : 5/14 : 3/28
4 : 10 : 3

b) Tom and Bob meet every 4 mins, ie in the multiply of 4.
21 / 4 = 5.25, therefore we use 6x4 = 24 mins
After 24 mins, Tom ran 24/7 rounds = 4200m
Each round = 4200 x 7/24 = 1225m

Therefore, in 24 mins, Kelvin ran 5/14 x 24 x 1225 = 10,500m

Hi mathsmonster.The answer for section b is different from the one gn in the answerkey:It states the follw:
21 min = 4200m
7min = 4200/21x7
1 round = 1400m
Kelvin completed 2.5 rounds in 7 min, so, 2.5 x 1400 = 3500m.(ANS)
I dint understand the part writted in red. Pl.explain.Sorry 2 trouble u again..[/quote]a)

Time ratio
Tom : Bob = (7 – 4) : 4 = 3 : 4
Tom : Kelvin = (7 – 2) : 2 = 5 : 2
Tom : Kelvin : Bob = 15 : 6 : 20

Speed ratio
Tom : Kelvin : Bob = 1/15 : 1/6 : 1/20 = 4/60 : 10/60 : 3/60 = 4 : 10 : 3

b)

In 21 mins; Tom completed 3 rounds
1 round = 4200m/3 = 1400m
If time is constant
Distance ratio => Tom : Kelvin : Bob = 4 : 10 : 3
4u = 4200
1u = 1050m

After 21 mins; Kelvin had run 10u (10 x 1050m) = 10500m.

# The part in red is given in the qn. Tom takes 7 mins to complete 1 round. So, in 21 mins he would have completed 3 rounds which is 4200m.

From distance ratio we know that in the same time, Tom travels 4u Kelvin would have covered 10u (Kelvin's speed is 2.5 times Tom's speed)

If Kelvin completes 1400m x 2.5 = 3500m in 7 mins.
He will complete 3500m x 3 = 10,500m in 21 mins.

I agree with MM's answer.

[liketoeat]

Tang:

Dharma:

[quote=\"Vanilla Cake\"]
Since this is a P6 question then use algebra which is good enough to solve and gain full marks.
Let number of cubes added be n
( 5x1.58 )+( nx1.6 )=( n+5 )x1.595
n=15
Number of cubes added = 15

Hope other members will forward with non-algebraic approach so that readers of this forum can learn.

http://www.postimage.org/image.php?v=aVb175J

Increase in average --> 1.595 - 1.58 = 0.015

Total increase --> 0.015 x 5 = 0.075 kg

Decrease in average --> 1.600 - 1.595 = 0.005

So number of cubes added --> 0.075/0.005 = 15 cubes

15 cubes were added.[/quote]Thank you all for the solutions.

[Hifive]

Hi Vanilla Cake


Thanks for the help with my question.

[Almighty]

Maths Monster:

For part (b), I may have assumed wrongly that Tom and Bob meet at 24 mins. But the fact is that Tom and Bob does not meet at 21 mins. They meet every 4 mins, ie multiply of 4.

As for the answer given, the distant that Kelvin ran is for 7 mins which seems to contradict the question which states after 21 mins.

Based on the two points above, I am not sure if the question is correctly stated. Perhaps, you can check again on the question to verify it is correct. BTW, where is this question taken from?

Cheers,
MM

Thank you for yr detailed explanation MM.Its from
Andrew ER's Worksheet P6 Assessment book Editioon 2009.I also went wrong in tht step n dint know how is \" the distant that Kelvin ran is for 7 mins which seems to contradict the question which states after 21 mins.\"