Tutor MathsGuru: Ask me for your burning Maths questions!

[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.

[parentof3]

Dharma:

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.

Thanks dharma & mathsguru!

[Dad fm East]

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

Hi MathsGuru,
Glad you are back. Thanks for your help. :thankyou: :lol:

[Dad fm East]

Hi trytry,

Thanks for your help too.

:thankyou:

Cheers
Dad fm East

[mathsguru]

Dharma:

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.

Hi Dharma,

Ah...so it's $281!! Hehe...you're brilliant!! Thanks for pointing that out~~

Cheers,
MathsGuru

[Dharma]

mathsguru:

Dharma:

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.

Hi Dharma,

Ah...so it's $281!! Hehe...you're brilliant!! Thanks for pointing that out~~

Cheers,
MathsGuru

Not brilliant lah, maths guru... 218 + 342 = 560 ...not divisible by 7 ...must be input error!!

[OngMum]

Hi mathsguru, I have a P6 question that needs your assistance to solve.

Looks like model drawing cannot be applied. Time factor is required to be identified. Thanks alot!

Qn : Sulin is given $5 more pocket money than Meihua each week. They each spend $12 per week and save the rest. When Sulin saves $60, Meihua saves $20. How much pocket money does each girl have per week?

[OngMum]

Hi mathsguru, I understand not all qns can be solved by model drawing. Like one qn that my daughter encountered this week, for example needs to adopt check and balance method as there is unknown information. Is there any tips on identify such qns after reading once? Thanks.

[mathsguru]

OngMum:

Hi mathsguru, I have a P6 question that needs your assistance to solve.

Looks like model drawing cannot be applied. Time factor is required to be identified. Thanks alot!

Qn : Sulin is given $5 more pocket money than Meihua each week. They each spend $12 per week and save the rest. When Sulin saves $60, Meihua saves $20. How much pocket money does each girl have per week?

Hi OngMum,

Here's my solution. Though drawing models is not a must, I feel that drawing out models helps me in visualising the problem better. For instance, after drawing out the models, I can see clearly that the difference between their savings is $5 per week.

http://www.postimage.org/image.php?v=Pq1x0wNA

Cheers,
MathsGuru

[mathsguru]

OngMum:

Hi mathsguru, I understand not all qns can be solved by model drawing. Like one qn that my daughter encountered this week, for example needs to adopt check and balance method as there is unknown information. Is there any tips on identify such qns after reading once? Thanks.

Hi OngMum,

I do agree that not all questions can be solved by model/diagram drawing. Sometimes, there's no need for it or sometimes, it is simply of no help.

Although I can't spell out all the criteria for identifying a question which needs models/diagram, I can list down some that I can think of right now:
1. When ratio or fractions or percentage or age is involved
2. \"Before and after\" questions involving the above topics (e.g. give some sweets away to another person, some men left and some women entered the room and then the ratio changed, etc)
3. Comparison question involving 2 or more people and their items (e.g. A has 12 marbles more than B and C has 10 marbles more than B. Total = 70 marbles.)
4. Certain speed questions (these are usually more of diagrams to visualise rather than unitary models)
5. When questions have phrases like \"twice as much\", \"thrice as much\", \"half of\", etc.
6. Certain money problems, especially when it's a complicated question that has a bit of info on quantity and a bit of info on value (e.g. Went shopping with $360. Bought some shirts and skirts. Had $8.50 left. Bought 3 fewer skirts than shirts. Each skirt is $15.50 more than a shirt. How many shirts was bought?)

Hope you can relate to the types of questions I described above!

Just to add, many students find ratio/fraction/% questions more challenging and they usually get stuck in trying to draw out the models. And (unfortunately!) for these topics, models are usually the best way to solve the problems since simultaneous equations are not taught in Primary School. I guess that's why you find me using diagrams/models alot in my solutions because the questions posted are all mostly from these topics.

Well, in any case, for most questions, I usually encourage my students to use \"guess & check\" as the last resort. Even for questions like \"There are 85 rabbits and chickens in a farm. Ali counted 220 legs in total. How many rabbits and how many chickens are there?\", there's no need to use guess & check or models. We can use logic to deduce the correct answer in just 3-4 steps.

So, in my personal opinion, there's no hard & fast rule in solving maths questions. There're usually at least a couple of methods that we can use - just that there may be one that is simpler/shorter.

All I can say is the more types of questions we're exposed to through practice, the more adept we become in identifying the best methods to use to solve them. Hee...I guess there's no short cut in the pursuit of excellence...

Cheers,
MathsGuru