Elementary School Math Problems-2

Algebra Level 1

A teacher has 30 pens and 45 pencils that he wants to give to his students. If each student were to receive the same number of pens and the same numbers of pencils with none left over, then what is the maximum number of students that this teacher could have?

Image credit: Wikipedia Pens Pencils


The answer is 15.

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29 solutions

S W
Aug 27, 2014

Greatest Common Divisor of 30 and 45 is 15.

no solutions indeed. just mental math

Miguel Malicdem - 6 years, 9 months ago

2 pen for and 3 pencil for every child

Prencess Meneses - 6 years, 8 months ago

basically, 30/45 = 2/3 => each student will have 2 pens and 3 pencils

Jenny Darling - 5 years, 4 months ago

HCF of 30 and 45 is 15

sachin patil - 6 years, 8 months ago

Am I the only one to realize that pencils can easily be broken in half? 1.5 pencils and a pen to each student results in 30 students able to take notes. There's little chance this elementary school teacher has only 15 pupils.

Jeanclaude Tremblay - 5 years, 5 months ago

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Me too...entered 30 and got wrong. Its not told anywhere that we need to distribute all. So just thought 30 pencils and 30 pens among 30 students.

Vijay Kumar - 5 years, 4 months ago

I think ur right

nadhi sathee - 6 months, 2 weeks ago

how to slove the problem

dhanalakshmi mani - 6 years, 9 months ago

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take HCF of them

Sàháj Siñgh - 6 years ago

1.5 pencils mean 1 pencil and it's half mean a broken pencil

Debdeep Sen - 5 months, 3 weeks ago

the question didn't imply that the teacher has to give away "all" his pens and pencils.. so he could have given away 30 pairs of pens and pencils for each student, having 15 pencils left with him.. then the maximum number of student he could have was to be 30.

Faried Omarah - 6 years, 9 months ago

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It is written "with none left over"

Kelvin Tan Jin Loong - 6 years, 9 months ago

Even that the question didn't imply that, the maximum number would be 45. He could give 1 pencil to each student and 0 pens. But as it is written "with none left over" the maximum is the gcd(30,45)=15.

Daniel Rabelo - 6 years, 9 months ago

the question say with none left over!!!

Naimesh Jariwala - 6 years ago
Kashif Ahmad
Aug 29, 2014

The problem can be very easily solved using the concept of greatest common divisor,but let's look at it in other way.(You'll find out that this 'other way' is just another way of using the same concept of GCD. Let n be the no. of students,x be the no. of pens and y be the no. of pencils that each of them receive. Then for no left overs,we must have, n(x+y)=45+30=75 Also, nx=30 and ny=45. Thus,x/y=30/45=2/3 Now,n=75/(x+y). To make n maximum,x+y must be made minimum and from above,we find that min(x+y)=2+3=5 because x and y must be natural numbers.This is where I've 'unknowingly' invoked the law of GCD.(Mathematics is awesome). Finally,max(n)=75/5=15

congratulation, your solution is excellent & everybody can understand easily

azadali jivani - 5 years, 10 months ago
Isharth Rastogi
Aug 29, 2014

lol. max pens are 30 so the max students cant be greater than 30. Now the greatest number below 30 that can be divisor of 45 with no remainder is 15.. so 15 students

Lilith Jae
Aug 28, 2014

The highest common factor of 45 and 30, which is the biggest number of students equally receiving pens and pencils, is 15

no comment

vasavi yarramsetti - 6 years, 9 months ago

The prime factorizations of 30 30 and 45 45 is

30 = 2 × 3 × 5 30=2 \times 3 \times 5

45 = 3 2 × 5 45 = 3^2 \times 5

So the Greatest Common Divisor is 3 ( 5 ) = 3(5)= 15 \color{#D61F06}\large \boxed{15}

Tytan Le Nguyen
Jan 11, 2015

It's just the GCD of 30 and 45, which is 15.

Víctor Martín
Aug 29, 2014

What does the asymptote tell the curve?

Don't touch me.

Nandish Immortal
Aug 28, 2014

HCF of 30 and 45. 15 students with 2 pens and 3 pencils each

John Altyre
Jun 6, 2020

To find out the answer you have to find most common multiple between 30 and 45 and the answer is 15. I am so happy that now finally I have time to solve funny quizzes and spend time on this BRILLIANT page, however it wasn't always like that I had a lot of task connected with writing essay, etc, and this web site really helped me https://aussieessaywriter.com.au/ if you have such problem. RECOMMEND YOU!

G C D ( 30 , 45 ) = 15 GCD(30,45)=\boxed{\large{15}}

Charlie Marom
Mar 30, 2018

The highest common multiple of 30 and 45 is 15

Akul Sharma
Jun 18, 2016

G.C.D(30,45)=15.....there can be maximum of 15 students..and each student will get 2 pens and 3 pencils

Anderson Lc
Dec 5, 2015

X+Y=30 X-Y=45 The difference of this number is 15. Answer is 15. You can solve this way using adding metod or logic,Because only 15 students can receive the same quantity of pens and pencils.

Christopher Unrau
Nov 25, 2015

We have 30 pens and 45 pencils. If we're to hand them out equally with none left over, we can assume that the MAXIMUM amount of students can be represented by the largest common factor of 30 and 45. This number is 15, so there can be a maximum of fifteen students.

Asep Fetriady
Oct 6, 2015

GCD(30,45)=15

Sarah Shams
May 22, 2015

Highest common factor. All 15 students each would receive 2 pens and 3 pencils each.

Vedanth Bhatnagar
May 22, 2015

Can we solve this using Combinatorial methods? I have observed that, if we were to have 30 and/or 45 students, the Pigeonhole principle would come into play.

Vishal S
Jan 6, 2015

Since gcd ( 30 , 45 ) \gcd(30,45) is 15

Therefore the maximum number of students that he could have is 15

For maximum number of equal amounts of any two or more objects will be the HIGHEST COMMON FACTOR, which in this case is 15

Look for the greatest common factor: 30 = 5 x 3 x 2 45 = 5 x 3 x 3 GCF = 5 x 3 = 15 What's left after removing the GCF from the equation is how much of each item (ie. 2 pens and 3 pencils) each student is to receive.

Kabir Bagai
Oct 12, 2014

GCF of 45 and 30 is 15

Krishna Garg
Sep 27, 2014

we find H.C.F. of 30 and 45 that is 15,so no of students is 15 ANS K.K.GARG,India

Hon Ming Rou
Sep 1, 2014

The highest common factor of 30 and 45 is 15. So, the answer is 15.

Muhammad Asyraf
Sep 1, 2014

45 - 30 = 15 It is as easy as ABC

Samar Mostafa
Aug 29, 2014

maximum diviser of 30 and 45 is 15

Mostafa Algammal
Aug 29, 2014

it's something in ratio factor to keep reminder equal Zero
30%15=0 ...... 45 %15=0

Pijush Biswas
Aug 29, 2014

Its easy.... 15. :)

Aman Sharma
Aug 28, 2014

Hey who edited it and how

Eka Kurniawan
Aug 27, 2014

Greatest common divisor of 30 and 45 is 15.

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