B.2 Relationship of three integers (distribution)

There are three integers A, B, and C. 

The product of A and B is 408, the product of A and C is 336, and the sum of B and C is 62. 

Find the integer B.




Answer
34

Solution
This problem is denoted by a formula, it is 
A × B = 408, A × C = 336, and B + C = 62.

A × B + A × C = 408 + 336 = 744  

According to the distributive principle, this formula is to be A × (B+C) = 744. 

Since it is B + C = 62, it is A × 62 = 744. 

Therefore, A = 744/62 = 12. 

B = 408/12 = 34 .