Problem #PRU-100626

Problems Methods Algebraic methods Counting in two ways

Problem

There are some cannons in every fortress on the Cannon Island. The star marks the Grand Fortress, the capital, and the 10 circles mark 10 smaller fortresses. The total number of cannons located in all the fortresses along the east-west road is known to be \(130\). The total number of cannons along each of the other 3 roads is \(80\). Also it is known that there is a total of \(280\) cannons in all the fortresses. How many cannons are in the capital?