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 $10$.
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