(x- 1)x+x(x+ 1)+(x- 1)(x+ 1)= 146-& gt; 3x^2= 147->; x=7
6 barrels for breakfast, 7 barrels for lunch and 8 barrels for dinner.
How to solve it by arithmetic?
Arithmetically, because 146 is the sum of three close products of two numbers, each product of two numbers should be close to 146/3≈48=6*8, so it is easy to think of trying with numbers of 6, 7, 8 and 3.