
By: Aliah (offline) Friday, October 15 2010 @ 07:54 AM CDT (Read 4494 times)



Aliah 
There is a maths problem which I can't solve.
Can anyone please help me?
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: AliahThere is a maths problem which I can't solve.
Can anyone please help me?
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_91I 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
1x63=3
2x63=9
3x63=15
4x63=21
5x63=27
6x63=33
So answer is 33 pens.
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=65=1
Now based on formulae
(3+3)%1=6
total=6*5+3=33
or
6*63=33
Hope u unnderstand
U can buy maths olympiad book for these non routine sums
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.
Can anyone please help me?
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



