Maths question - how to solve by model method?

[Sosaria]

Teachers and primary-level maths experts, fall in...

 

Square table can seat 4, while round table can seat 6. Restaurant has total 40 tables, square and round, and can seat 184 people. How many square, and how many round tables??

 

Solving by simultaneous equations is easy, but how to solve by model method?

 

[Sosaria]

So far the only way I came up with to solve the question, without using algebraic simultaneous equations, is as follows:

 

(1) Since a square table seats 4, and a round table seats 6, every 3 square tables can be converted to 2 round tables, for the reduction of 1 table.

 

(2) Total 184 people can be divided nicely by 4, and not 6, so 184 / 4 = 46, i.e. if the restaurant only had square tables, it would need 46 of them to seat everybody. But this exceeds the total of 40 tables desired by 6!!!

 

(3) Now we have to cut down the number of tables by 6, so we rely on our observation in Step (1), i.e. to minus off 6 tables, we'd need to convert 18 (3x6) square tables into 12 (2x6) round tables.

 

(4) Having done that, we have 46-18 = 28 square tables left, with addition of 12 round tables. Total 40 tables! Seats 184!!

 

Is there a more elegant / organised method using models that are drawn out, i.e. for a primary-level student to write down as the solution during exam?

[Qpik]

this is a method termed as "guess & check"

 

i start off with 20 square (80pax), 20 round (120pax) = 200pax, from here can see we need to adjust & work towards 184pax.

 

so, i adjusted : 22 square (88pax), 18 round (108pax) = 196pax.

 

eventually, i worked down to 28 square (112pax), 12 round (72pax) = 184 pax.

 

my ger did learn a simple 4 steps formulae to tackle such qtns but i don't hv it to share.

[Mcf777]

nb, i also got knocked out last night by my childred p3 maths.

for this question, use the guess and check method.

 

Square I No of person I Round I No pf person I Total no of person I Check I

30 / 120 / 10 / 60 / 180 / X

29 / 116 / 11 / 66 / 182 / X

28 / 112 / 12 / 72 / 184 / correct

[Sosaria]

I see. So this is kind of like solving through iterations. Looks better and simpler for a kid to understand. Thanks.

 

The tricky part is that the kid need to learn which direction to do the "adjustment" and the initial values to start with.

[Sosaria]

nb, i also got knocked out last night by my childred p3 maths.

for this question, use the guess and check method.

 

Square I No of person I Round I No pf person I Total no of person I Check I

30 / 120 / 10 / 60 / 180 / X

29 / 116 / 11 / 66 / 182 / X

28 / 112 / 12 / 72 / 184 / correct

 

Yes, the question I posted is also P3 , supposedly set by "elite/branded" school.

 

Just one stubborn question in the paper for which I cannot present a "neat" solution.

Edited April 26, 2012 by Sosaria

[Mcf777]

last night, im stuck with a question that i had never learn it during my school days.

but after looking at the formula, i have managed to figure it out.

 

Example :

Question A : How many stars at Box 37?

Question B : 184 stars is at which Box ?

 

Box 1 : 1 star

Box 2 : 4 stars

Box 3 : 7 stars

Box 37 : How many stars ?

Box ? : 184 stars

 

 

 

 

[Coltplussport]

Teachers and primary-level maths experts, fall in...

 

Square table can seat 4, while round table can seat 6. Restaurant has total 40 tables, square and round, and can seat 184 people. How many square, and how many round tables??

 

Solving by simultaneous equations is easy, but how to solve by model method?

 

We use 40 x 4 =160

 

So there is need to accommodate another 184-160 = 24 persons.

 

So for every round table can sit 6 - 4 = 2 more persons, there will be 24/2 =12 round tables.

 

40-12=28 square table.

[Fondue]

Given 40 tables, SQ=4pax, RD = 6 Pax, 184 total pax

 

Assume all SQ table => 40 x 4 = 160 pax max.

Need 184-160 = 24 more seats.

 

SInce RD has 2 more seats than SQ, will need 24/2 = 12 RD

 

Therefore, there are 12 RD and 28 SQ.

[Ender]

We use 40 x 4 =160

 

So there is need to accommodate another 184-160 = 24 persons.

 

So for every round table can sit 6 - 4 = 2 more persons, there will be 24/2 =12 round tables.

 

40-12=28 square table.

Again you gave very clear explanation. as the one you gave in my other thread on the farm animals...

[Espresso]

This is how i will teach a primary kid...

 

 

There are altogether 40 tables. I like square tables better! I think they are nicer than round tables. Each square table can seat 4 person. But if there are 40 square tables, we can only seat 40 x 4 = 160 people. We need to seat 184 people. Oh gosh we are still short of seats for 24 people!!!

 

A round table can seat 6 people. A square table can set 4 people. Since we do not have enough seat for 24 peole, we will need to replace some of the square tables with round tables. For every round table we use to replace square table, we can seat 2 extra people. Now, do you remember how many extra people we need to seat? Yes we need to seat 24 extra people. So if one round table can add 2 extra seat, how many round tables do we need to add 24 seats? Yes thats right, it's 24 divided by 2 = 12 rounds tables.

 

So we will need to replace the square tables with 12 rounds tables. If you remember, at first we have 40 square tables. After we replace 12 square tables with round tables, how many square table do we have left? Yes thats right, we have 28 square tables. So total we have 28 square tables and 12 round tables.

[Raymondism]

Teachers and primary-level maths experts, fall in...

 

Square table can seat 4, while round table can seat 6. Restaurant has total 40 tables, square and round, and can seat 184 people. How many square, and how many round tables??

 

Solving by simultaneous equations is easy, but how to solve by model method?

 

 

imagine 40 tables all square.. therefore can seat up to 160 <-- not true still 24 standing

 

hence the number of round tables gotta be 24 / 2 = 12

 

therefore... there are 12 round tables and (40-12=) 28 square table...

 

not sure what model u talking abt

[Ronleech]

Take 184/4 = 46 (as 4 is the basic of a sq table) and 184 cant divide by 6 which will give you remainder.

 

46 tables needed if all use sq.

 

6 table extra = 6 x 4 = 24 pax wihtout a seat is use rsq table. As round table can take 2 extra pax. 24/2 = 12 thus needed 12 table which can accomodate 2 extra pax each.

 

40-12 = 28 sq

40-28 = 12 Round

 

But this is using logic...anyway to use model?

Edited April 26, 2012 by Ronleech

[West_end]

1 square table sits 4

 

1 round table sits 6

 

Total nos of tables = 40

 

Total seats = 184

 

(4 x s) + (6 x r) = 184 ------ (1)

 

s + r = 40 ----- (2)

 

From Eqn 1,

4s + 6r = 184

4s = 184 - 6r

Hence s = 184 - 6r / 4

 

subst. into eqn 2,

 

184 - 6r / 4 + r = 40

46 - 1.5r + r = 40

46 - 40 = 1.5r - r

Hence, r = 12 = round tables (Ans)

 

Since r = 12 , s will be = 40 - 12 = 28 square tables (Ans)

 

 

[Ronleech]

last night, im stuck with a question that i had never learn it during my school days.

but after looking at the formula, i have managed to figure it out.

 

Example :

Question A : How many stars at Box 37?

Question B : 184 stars is at which Box ?

 

Box 1 : 1 star

Box 2 : 4 stars

Box 3 : 7 stars

Box 37 : How many stars ?

Box ? : 184 stars

 

Interval of each box is 3, apart from box 1.

 

Qns 1 Box 37

 

37 -1 = 36

36 x 3 = 108

108 + 1 star in box 1 = 109

 

 

Qns 2 Box ? = 184 stars

 

184 - 1 (star in box 1) = 183

183 / 3 = 61

61 + 1 (box 1) = 62

 

 

[Sosaria]

1 square table sits 4

 

1 round table sits 6

 

Total nos of tables = 40

 

Total seats = 184

 

(4 x s) + (6 x r) = 184 ------ (1)

 

s + r = 40 ----- (2)

 

From Eqn 1,

4s + 6r = 184

4s = 184 - 6r

Hence s = 184 - 6r / 4

 

subst. into eqn 2,

 

184 - 6r / 4 + r = 40

46 - 1.5r + r = 40

46 - 40 = 1.5r - r

Hence, r = 12 = round tables (Ans)

 

Since r = 12 , s will be = 40 - 12 = 28 square tables (Ans)

 

Yes, that's how we learned it in the olden days, using algebra and simultaneous equations. But nowadays primary school has more or less done away with such "rote" methods in teaching maths. Because at primary level, students don't know what is x, y and why must eliminate one unknown, etc. They'll just blindly follow a set of steps and get the answer. Good for exams, but understanding is doubtful.

[Sosaria]

We use 40 x 4 =160

 

So there is need to accommodate another 184-160 = 24 persons.

 

So for every round table can sit 6 - 4 = 2 more persons, there will be 24/2 =12 round tables.

 

40-12=28 square table.

 

Yup, this method you and several others who posted later proposed, looks more straightforward. It's more or less the same as the steps I outlined, but my way of doing it was more long-winded, i.e. find excess tables, remove those excess tables which resulted in some people left unseated, and the rest follows.

 

Thanks.

[Fishman]

Try this Pri 5 question without using algebra or cross multiplication.

 

A and B has some money in the ratio of 13:8. After both of them gave away $133 each, the ratio of money becomes 4:1. How much money does A have at first?