1) x, y direct proportionale cu 5 si 7
m. a. = 29,4
x/5=y/7=k => x=5k si y=7k
(x+y)/2=29,4 => (5k+7k)/2=29,4 =>
12k/2=29,4 => 6k=29,4 =>
k=4.9 => x=5×4,9 => x=24,5
=> y=7×4,9 => y=34,3
2) x, y direct proportionale cu 2 si 3
c.m.m.m.c.=36
x/2=y/3=k⇒ x=2k⇒x=12
y=3k⇒y=18
c.m.m.m.c. a lui 12 si 18=2²·3²=4·9=36
2k+3k=36-k
2k+3k+k=36
6k=36/6
k=6
3) a, b, c invers proportionale cu 0,(3); 0,5; 0,2
p=63cm
a+b+c=63
a×0,(3)=b×0,5=c×0,2=k
0,(3)=3/9=1/3
0,5=5/10=1/2
0,2=2/10=1/5
a/3=b/2=c/5=k
a=3k ; b=2k ; c=5k
3k+2k+5k=63 => 10k=63 => k=6,3
a=3×6,3 => a=18,9
b=2×6,3 => b=12,6
c=5×6,3 => c=31,5
4)x, y direct proportionale cu 0,(3) si 0,1(6)
y, z invers proportionale cu 15 si 9
x, y, z € N
0,(3)=3/9=1/3
0,1(6)=(16-1)/90=15/90=1/6
3x=6y=k => x=k/3 ; y=k/6
15×y=9×z=k => y=k/15 ; z=k/9
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