Question

Daca 3a + 7b supra 8a + 5b = 64 supra 75 , aflati valoarea raportului a supra b .

Answer 1

(3a+7b)/(8a+5b)=64/75

64(8a+5b)=75(3a+7b)

512a +320b = 225a + 525b

512a-225a=525b-320b

287a= 205b

a/b= 205/287

Answer 2

facem o inlocuire a/b=t
de unde a=bt
deci avem
3*bt+7b 
------------
8*bt+5b
dam factor comun pe b si simplificam
si obtinem 3t+7/8t+5=64/75
facem calculele 225 t+525=512t+320
adica 287t=205
t=205/287.
adica a/b=205/287.