Question

Determinati nr. a,b,c stiind ca a+b supra 5 =b+c supra 7= c+a supra 8 si 5a+3b+2c=62

Answer 1

(a+b)/5 = (b+c)/7
7(a+b) = 5 (b+c)
7a + 7b = 5b +5c    
7a +2b = 5c
 
(a+b)/5 = (c+a)/8  
8(a+b) = 5(c+a)     
8a + 8b = 5c +5a   
3a +8b =5c

7a + 2b = 3a +8b   
4a = 6b            
2a = 3b        
b = 2a/3

(b+c)/7 = (c+a)/8   
8(b+c) = 7(c+a)   
8b + 8c = 7c + 7a    
c = 7a - 8b= 7a - 8·2a/3 = 5a/3

5a + 2a + 10a/3 = 62   
15a + 6a + 10a = 186   
31a = 186   
a = 6 
b = 4 
c =10