Tutor MathsGuru: Ask me for your burning Maths questions!

[mathsguru]

YLH88:

Hi mathsguru,

http://www.postimage.org/image.php?v=Pq1eShZA
In the above question,
1) the 2th and 4th diagram are referring to Andrew's model right ?
2) how did you get the step 4 x (12 + 18 ) ?

Hi YLH88,

Hope you can understand my solution better after reading the below...do let me know if you still have any doubts.

1. The 1st 2 sets of diagrams (1 set = both Kenny and Andrew) are illustrating the 1st 2 statements of the question.

2. For this kind of question, it is essential to express the 1 of the scenario in terms of the other scenario.

3. From the 2nd set of diagram, we realise that Andrew’s original no. of marbles (denoted by blue colour) is definitely more than 12 (i.e. the no. of marbles Andrew gives Kenny). Hence, we draw Andrew’s marbles in 2 parts – 1 unit + 12.

4. From here, we can redraw the 1st set of diagram (refer to the 3rd set of diagram). If Kenny gives 18 marbles to Andrew, Andrew will have 1 unit + 12 + 18. Since Kenny will have 3 times as many marbles as Andrew after giving away 18 marbles to Andrew, Kenny will have (1 unit + 12 + 18 ) x 3.

5. Notice that we are now using 1 unit as the common unit of comparison for both scenarios. That is the key in solving such questions.

6. Now, let’s express Kenny’s original no. of marbles in terms of this common unit. It will be (1 unit + 12 + 18 ) x 3 + 18. Note that we add back the 18 marbles to obtain Kenny’s original no. of marbles.

7. Lastly, we should make use of this new way of drawing out Kenny’s original no. of marbles to redraw the 2nd set of diagram (refer to the 4th set of diagram). Note that we should include another 12 marbles from Andrew and Andrew’s share should just be 1 unit as he would have given away the 12 marbles.

8. Since Kenny should have 9 times as many marbles as Andrew in the 4th set of diagram, Kenny’s share of marbles should be equivalent to 9 units. However, from the 4th set of diagram, Kenny has 3 units + (12 + 18 ) x 4. Hence, logically, (12 + 18 ) x 4 should make up 9 – 3 = 6 units.

9. From here, we can easily calculate out 1 unit equals to how many marbles.

Cheers,
MathsGuru

[mathsguru]

headache:

Question : FRom his pocket money, Victor spent thrice the amount that he could save every month. When he spent $20 less, he found he could save $40. How much was his pocket money?

Hi Headache,

Here's my solution. Hopefully you find it clear enough to understand.

http://www.postimage.org/image.php?v=Ts6xzHS


MathsGuru

[mathsguru]

YLH88:

Hi, need ur help with the below question :


At present, Ronald is 3 times as old as his sister. In 22 years' time, Ronald's age will be 19 years less than twice his sister's age. How old is Ronald now ?

Hi YLH88,

Please see my solution below. Hope it helps!

http://www.postimage.org/image.php?v=aV1cSFU0


MathsGuru

[kiasimom]

Hi mathsguru,


Happy 2010 to you. Hope you have fully recovered from your sickness.

We look forward to having you here at KSP to help us

Take care :celebrate:

[mathsguru]

Dad fm East:

1) At first, Jonathan had 2/3 as many stamps as Kevan. After Jonathan bought another 8 stamps and Kevan lost 5 stamps, Jonathan now has 4/5 as many stamps as Kevan. Find the number of stamps Jonathan had at first.


2)At a school carnival, there were 520 more girls than boys. 1/8 of the girls and 1/5 of the boys left the carnival. In the end, there were 488 more girls than boys.
a) How many more girls left?
b) How many children were there in the carnival at the end?

Hi Dad fm East,

Here you go...hope the diagrams are clear enough for you and your ds to understand!

http://www.postimage.org/image.php?v=aV1dbZui

http://www.postimage.org/image.php?v=aV1dbW_9

Cheers,
MathsGuru

[mathsguru]

parentof3:

The cost of 3 similar watches and 4 similar rings is $218. Nancy bought 4 such watches and 3 such rings for $342. What is the cost of 2 such watches and 3 such rings.

Hi Parentof3,

Apologies but I can't seem to solve this question. If I'm not wrong, the question probably has an error because I can't obtain 2 positive answers for the prices. My answer is $102 for 1 watch and -$22 for 1 ring which is not logical. In any case, using the answers above, 2 watches and 3 rings will cost $$138.

Any one else who can solve this without ending up with a negative answer? Will be really insightful to see the solution!


MathGuru

[mathsguru]

kiasimom:

Hi mathsguru,


Happy 2010 to you. Hope you have fully recovered from your sickness.

We look forward to having you here at KSP to help us

Take care :celebrate:

Thanks alot Kiasimom! Still coughing a little, but at least I see signs of recovery already. Water is my best friend, especially since I have to talk alot during lessons...haha...

Happy 2010 to you too!

Cheers,
MathsGuru

[trytry]

Before


girls [5u+65][5u+65][5u+65][5u+65][5u+65][5u+65][5u+65][5u+65]


boys [8u ][8u ][8u ][8u ][8u ]----------------------520--------------------

(split the boys into 40 units and rearrange the girls as above)



After

girls [5u+65][5u+65][5u+65][5u+65][5u+65][5u+65][5u+65]


boys [8u ][8u ][8u ][8u ]--------------------488-------------------



girls: 5ux7 + 65x7 = 35u + 455

boys: 8ux4 =32u

35u + 455 -32u = 488

3u = 488-455
= 33
1u = 33 / 3 = 11

Total children at the end= 32u + 35u + 455
= 67u + 455
= 67x11 + 455
= 737 +455
= 1192


easier to understand?

mathsguru:

Dad fm East:

1) At first, Jonathan had 2/3 as many stamps as Kevan. After Jonathan bought another 8 stamps and Kevan lost 5 stamps, Jonathan now has 4/5 as many stamps as Kevan. Find the number of stamps Jonathan had at first.

2)At a school carnival, there were 520 more girls than boys. 1/8 of the girls and 1/5 of the boys left the carnival. In the end, there were 488 more girls than boys.
a) How many more girls left?
b) How many children were there in the carnival at the end?

Hi Dad fm East,

Here you go...hope the diagrams are clear enough for you and your ds to understand!

http://www.postimage.org/image.php?v=aV1dbZui

http://www.postimage.org/image.php?v=aV1dbW_9

Cheers,
MathsGuru

[YLH88]

Hi Mathsguru,


Thank you for the explanation and solution.

Hope you have fully recovered

[Dharma]

mathsguru:

parentof3:

The cost of 3 similar watches and 4 similar rings is $218. Nancy bought 4 such watches and 3 such rings for $342. What is the cost of 2 such watches and 3 such rings.

Hi Parentof3,

Apologies but I can't seem to solve this question. If I'm not wrong, the question probably has an error because I can't obtain 2 positive answers for the prices. My answer is $102 for 1 watch and -$22 for 1 ring which is not logical. In any case, using the answers above, 2 watches and 3 rings will cost $$138.

Any one else who can solve this without ending up with a negative answer? Will be really insightful to see the solution!


MathGuru

Hi mathsguru,

You’re right …. there's an error in qn. Think the cost of 3 watches & 4 rings should be $281 instead of $218.

3W + 4R = 281
4W + 3 R = 342
7W + 7R = 623
1W + 1R = 89
1R = 281 – 3(89) = 14
1W = 89 – 14 = 75

So, 2W + 3R = 2(75) + 3(14) = 192

Cost of 2 watches & 3 rings will be $192.