Try this Problem based on Algebra from Math Kangaroo (Benjamin) 2016 Problem 20
Luigi owns a few square tables and some chairs for his little restaurant. If he sets out his tables individually with 4 chairs each, then he is 6 chairs short. If he always puts two tables together to create a bigger table with 6 chairs, then he has 4 chairs left over.
How many tables does Luigi have?
Algebra
Arithmetic
Equation Solving
Mathematical Circle
Math Kangaroo (Benjamin) 2016 | Problem 20
10
Let us assume the number of tables and chairs are $x, y$ respectively.
Let's follow the given condition and construct the equations.
For the first case if he set table individually with 4 chairs each then he is 6 chairs short.
So, $4x-6=y$.
Now if he put two tables together with 6 chairs each, then he has 4 chairs left over.
So, $6\frac{x}{2}+4=y$.
Comparing the equation of hint 3 and hint 4 we get,
$4x-6= 3x+4$
So, $ x=10$
Hence the answer is $10$.
Publishing original scientific research in a peer-reviewed journal is an achievement many scholars work toward for years. Achieving this feat early in one's academic journey requires exceptional intellectual rigor, creativity, and persistence. Aaditya Punatar and Muskan Sadana have reached this remarkable milestone, successfully publishing their collaborative research paper in the prestigious Journal of Emerging Investigators […]
Her project on quantum-accelerated Steiner trees for 15-minute cities earned a place among the finalists at the world's largest pre-college STEM competition. Prishaa Shrimali of Marymount School of New York, was selected as a Grand Finalist at the 2026 Regeneron International Science and Engineering Fair (ISEF) in Phoenix, Arizona. Her project was Optimizing Urban Accessibility: […]
In 2026, the following Cheenta students have been successful for Indian Statistical Institute's M.Stat Entrance. They ranked within the first 50 in the entire country in these entrances. I.S.I. M.Stat Entrance
In 2026, the following Cheenta students have been successful for Indian Statistical Institute's B.Stat Entrance and Chennai Mathematical Institute's B.Sc. Math Entrance. They ranked within the first 200 in the entire country in these entrances. Most of these students attended the problem solving workshops regularly, which happen 5 days every week. CMI B.Sc. Math Entrance […]