Question

Suma a trei numere este 120. Aflați numerele, ştiind că sunt direct proporţionale cu numerele: a) 2; 3 şi 5; b) 3; 5 şi 7; c) 4; 3 şi 13; d) 5; 7 şi 12; e) 4; 6 şi 14.​

Answer 1

a) {a,b,c} d.p. {2,3,5}
a + b+ c = 120
a/2=b/3=c/5=k
a/2=k => a=2k
b/3=k =>b=3k
c/5=k => c=5k
2k+3k+5k = 120
10k=120
k=120/10
k= 12
a=2k => a=2 x 12, a=24
b=3k => b=3 x 12, b=36
c=5k => c=5 x 12, c=60

b) {a,b,c} d.p. {3,5,7}
a+b+c=120
a/3=b/5=c/7=k
a/3=k => a=3k
b/5=k => b=5k
c/7=k => c=7k
3k+5k+7k=120
15k=120
k=120/15
k=8
a=3k => a=3 x 8, a=24
b=5k => b=5 x 8 , b=40
c=7k => c= 7 x 8, c=56

c) {a,b,c} d.p. {4,3,13}
a+b+c=120
a/4=b/3=c/13=k
a/4=k => a=4k
b/3=k => b=3k
c/13=k => c=13k
4k+3k+13k=120
20k=120
k=120/20
k=6
a=4k => a=4 x 6, a=24
b=3k => b=3 x 6, b=18
c/13=k => c=13 x 6, c= 78

d) {a,b,c} d.p {5,7,12}
a+b+c=120
a/5=b/7=c/12=k
a/5=k => a=5k
b/7=k => b=7k
c/12=k => c=12k
5k+7k+12k=120
24k=120
k=120/24
k=5
a=5k => a=5x5, a=25
b=7k=> b=7x5, b=35
c=12k => c=12x5, c=60

e) {a,b,c} d.p. {4,6,14}
a+b+c=120
a/4=b/6=c/14=k
a/4=k => a=4k
b/6=k => b=6k
c/14=k => c=14k
4k+6k+14k=120
24k=120
k=120/24
k=5
a=4k => a=4x5, a=20
b=6k => b=6x5, b=30
c=14k => c=14x5, c=70