The dishes problem

Let the total number of guests be x

Number of dishes of rice used by the guests= x/2

Number of dishes of broth used by guests= x/3

Number of dishes of meat used by guests=x/4 

Since we know that the total number of dishes are 65
Therefore, there are many ways to find x, out of which two are discussed below :   
   

First method:                                                 Second Method:

x/2+ x/3  +x/4 = 65 (i) Hence, finding the lowest common multiple of 2,3,4 It comes out to be 12 On solving, We get, 6x + 4x + 3x = 780 13x = 780 x= 60, No. of guests = 60

We know that the Right-hand side is a whole number, therefore 2,3,4 must divide x  evenly, which is possible only if x is common multiple of 2,3, and 4. And, the lowest common multiple of 2,3,4  is 12. I found that on substituting 12 instead of x in the equation (i)  does not equal 65 Let’s try 24, 36, 48, 60, 72( multiples of 12) and substitute them to figure out which one satisfies the equation and gives us 65. On solving, I found that. x =60 satisfies x/2 + x/3 + x/4 = 65

Follow up questions:
I believe that it definitely matters if the students are offered examples, puzzles and told the history of mathematics from different cultures. In this way, they can learn cultures of their classmates as well. Nowadays the classrooms are very diverse and children from widely different backgrounds and cultures are at the same platform in the class. Hence, making them aware of each other's cultures along with cognitive math learning is an intelligent step towards creating an inclusive environment. Moreover, teaching math history of different cultures through puzzles or examples is an excellent way of acknowledging the great contributions of the mathematicians from different civilizations and this effort will certainly make the students realize that the math they are studying now is not the works of only one civilization or community, people all over the world have put efforts in to make it more meaningful.

I believe that word problems/ puzzles are really effective to break the monotonicity of solving regular math problems. I have seen some kids getting very excited to solve a puzzle introduced in the classroom. It adds the fun and the spark element in the student's routine. and I can relate that one feels immense happiness and a sense of accomplishment after solving the puzzle. In addition to this, I also believe that too many word problems and puzzles in the classroom can sometimes disinterest some students. The simple reasons for the disinterest can be an unwillingness to put in extra effort to solve the puzzle or think outside the box.