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 By: Aliah (offline)  Friday, October 15 2010 @ 07:54 AM CDT (Read 4611 times)
Aliah

There is a maths problem which I can't solve.

A group of pupils shared some pens. If each pupil got 5 pens, there would be 3 pens leftover. If each pupil got 6 pens, there would be a shortage of 3 pens. How many pens were there?

Thank You.

Newbie

Registered: 10/13/10
Posts: 3

 By: fish_91 (offline)  Saturday, October 16 2010 @ 01:23 AM CDT
fish_91

I use algebra to solve this question but apparently, I think p5 students have yet to learn algebra. I just encountered similar question to this when I was tutoring just now.

Anyways, to solve this by algebra,

let the no. of pupils be x
let the no. of pens be y

y - 5x = 3
y = 3 + 5x -------(1)

6x = y + 3
y = 6x - 3 --------(2)

sub (1) & (2) tgt
3 + 5x = 6x - 3
x = 6
-> y = 33

If you're are a tutor: Hmmm, perhaps you'd have known how to do this qns using algebra, but you need another method to teach right? haha.
If you're a tutee: As for me, I think I only know how to solve by algebra =X

Newbie

Registered: 05/11/10
Posts: 1

 By: MarianneEng (offline)  Saturday, October 16 2010 @ 04:00 AM CDT
MarianneEng

heres a solution from my hubby who teaches math.

A group of pupils shared some pens. If each pupil got 5 pens, there would be 3 pens leftover. If each pupil got 6 pens, there would be a shortage of 3 pens. How many pens were there?

The gap is 6 (3 pens leftover from scenario 1 vs 3 pens shortage from scenario 2)
The difference in the number of pens each pupil got is 1 pen.

Gap divided by difference = number of pupils
6 / 1 = 6 pupils
Pens = 6 x 5 + 3 = 33 (scenario 1)
Pens = 6 x 6 - 3 = 33 (Scenario 2)

Cheers

Newbie

Registered: 08/13/10
Posts: 1

 By: Patsy Goh (offline)  Friday, October 22 2010 @ 02:06 AM CDT
Patsy Goh

Can someone help with the below question:

Mrs Raju bought 20 bottle of milk and 5 boxes of cornflakes. If she bought these items at 20% discount, the amount she saved can buy 3 more boxes of cornflakes at the usual price. The usual price of 1 bottle of milk is \$2.15. What was the usual price of 1 box of cornflake?

Thanks

Newbie

Registered: 04/02/10
Posts: 4

 By: sethchew (offline)  Friday, October 22 2010 @ 08:36 PM CDT
sethchew

Quote by: Aliah

There is a maths problem which I can't solve.

A group of pupils shared some pens. If each pupil got 5 pens, there would be 3 pens leftover. If each pupil got 6 pens, there would be a shortage of 3 pens. How many pens were there?

Thank You.

5,10,15,20,25,30.........
each +3 and find whether if +3 again will divide by 6
30+3=33
33+3=36
36 divides by 6. 33 is the answer

Junior

Registered: 10/22/10
Posts: 15

 By: sethchew (offline)  Friday, October 22 2010 @ 08:39 PM CDT
sethchew

Quote by: fish_91

I use algebra to solve this question but apparently, I think p5 students have yet to learn algebra. I just encountered similar question to this when I was tutoring just now.

Anyways, to solve this by algebra,

let the no. of pupils be x
let the no. of pens be y

y - 5x = 3
y = 3 + 5x -------(1)

6x = y + 3
y = 6x - 3 --------(2)

sub (1) & (2) tgt
3 + 5x = 6x - 3
x = 6
-> y = 33

If you're are a tutor: Hmmm, perhaps you'd have known how to do this qns using algebra, but you need another method to teach right? haha.
If you're a tutee: As for me, I think I only know how to solve by algebra =X

well, there is a simpler ans. I know how to do by algebra but its abit long.
check my answer to his question

Junior

Registered: 10/22/10
Posts: 15

 By: kellywww (offline)  Monday, February 28 2011 @ 01:51 AM CST
kellywww

This is how my son was taught to solve:

1x5+3=9
2x5+3=13
3x5+3=18
4x5+3=23
5x5+3=28
6x5+3=33

1x6-3=3
2x6-3=9
3x6-3=15
4x6-3=21
5x6-3=27
6x6-3=33

There are 6 pupils.

Junior

Registered: 12/31/06
Posts: 21

 By: sokechan (offline)  Monday, February 28 2011 @ 02:09 AM CST
sokechan

You can actually draw a model.

The first model will be 5 similar units with 3 extra.

The second model will be 6 similar units with 3 units cut off.

Then, the difference between the units is one so 1 unit -> 3+3=6

5 units -> 6x5=30

30+3=33

OR

Multiples of 5: 5, 10, 15, 20, 25, 30
+3: 8, 13, 18, 23, 28, 33
Multiples of 6: 6, 12, 18, 24, 30, 36
-3: 3, 9, 15, 21, 27, 33

Junior

Registered: 02/25/11
Posts: 23

 By: shanthi (offline)  Sunday, March 06 2011 @ 09:10 PM CST
shanthi

hi This is EXCESS and SHORTAGE Problem

(EXCESS+SHORTAGE)% DIFFENCE =NUMBER OF UNITS
TOTAL=NUMBER OF UNITS*SHARES FOR EACH UNIT

excess=3
shortage=3
diffences of units=6-5=1

Now based on formulae

(3+3)%1=6
total=6*5+3=33
or
6*6-3=33

Hope u unnderstand

thanks

Junior

Registered: 12/31/06
Posts: 27

 By: NQS (offline)  Sunday, October 30 2011 @ 04:27 AM CDT
NQS

Quote by: Aliah
There is a maths problem which I can't solve.

A group of pupils shared some pens. If each pupil got 5 pens, there would be 3 pens leftover. If each pupil got 6 pens, there would be a shortage of 3 pens. How many pens were there?

Thank You.

3+3=6
6/1=6
6x5=30
30+3=33

ANS:33

Newbie

Registered: 09/16/10
Posts: 9

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