Answer to Question #189293 in Algebra for Aaqib

Question #189293

There are 100 pappadam at a kalyaana beef.. for a man .. u should give 10 pappadams.. for a woman .. u should give 5 pappadams .. and for a kid .. you should give 1/2 ( half ) pappadam.. and 100 people who went to the kalyanam got pappadam too .. how many men, women and children were there in this 100 people ?


1
Expert's answer
2021-05-06T16:18:51-0400

Let "x" denotes the number of men, "y" denotes the number of women and "z" denotes the number of kids. Then we have the following equations: "x+y+z=100" and "10x+5y+\\frac{1}{2}z=100." It follows that "z=100-x-y" and hence "10x+5y+\\frac{1}{2}(100-x-y)=100." Consequently, we have the equation "19x+9y=100." It is easy to see that "x=1" and "y=9" is a particular solution of this equation. Therefore, the general solution is "x=1+9t, y=9-19t, t\\in\\mathbb Z." In our case "0\\le x,y\\le 100" and hence "t=0." We conclude that "x=1,\\ y= 9, z=100-1-9=90" is a unique solution in our case. Therefore, there were 1 man, 9 women and 90 kids.


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