Question

Numerele a+3, b+4, c+5 sunt direct proportionale cu 3, 4 si respectiv 5. Aflati numerele a, b si c daca a+b+c=60. (Va rog repede)

Answer 1

a+b+c=60

{a+3,b+4,c+5} d.p {3,4,5}

a+3/3=b+4/4=c+5/5=k

a+3/3=k => a=3k/3

b+4/4=k => b=4k/4

c+5/6=k => c=5k/5

a+b+c=60(si acum inlocuim a,b si c cu valorile de mai sus)

3k/3+4k/4+5k/5=60

amplificam 3k/3 cu 4

aplificam 4k/4 cu 3

si va fi:

12k/12+12k/12+5k/5=60

24k/12+5k/5=60

amplificam 24k/12 cu 5

amplificam 5k/5 cu 12

120k/60+60k/60=60

180k/60=60

aplificam 60 cu 60

180k/60=360/60

Si acum facem produsul dintre mezi si extremi,adica va fi: 180k•60=360•60

10.800k=21.600 => K= 21.600/10.800

K=2

a= 3×2/3= 6/3=2

b=4×2/4= 8/4=2

c=5×2/5= 10/5=2