Question

Suma a trei numere nenule a,b,c este 21 . Stiind ca numerele 20% din a , 25% din b , 30% din c sunt direct proportionale cu numerele ( 1 supra 2) , ( 35 supra 48 ) si 1 , aflati numerele a,b,c !

Answer 1

a+b+c= 21

20% din a=  20/100 * a=  1/5 * a =  a/5

25% din b=  25/100 * b=  1/4 * b=  b/4

30% din c=  30/100 * c= 3/10 * c=  3c/10

a/5 ; b/4 ; 3c/10    dp    cu 1/2 ; 35/48; 1

a/5/1/2 = b/4/35/48= 3c/10/1 =k

a/5 * 2/1 = b/4 * 48/35 = 3c/10 * 1= k

2a/5 = 12b/35 = 3c/10 =k

a=5k/2

b=35k/12

c=10k/3

5k/2  + 35k/12 + 10k/3 = 21  aducem la acelasi numitor

30k + 35k + 40k = 252
105k=252

k= 252/105

a= (5 * 252/105)/2=  252/21/2=   252/21 * 1/2=  126/21 =6

b= (35 *252/105)/12= 252/3/12=  252/3 * 1/12= 21/3=7

c= (10*252/105) /3= (2*252)/21/3=  2*252/21 * 1/3=  2*84/21 =  2*4 =8