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Determinati numerele x , y , z , t , stiind ca sunt direct proportionale cu 2 , 3 , 5 , 7 , si 7x+ 5y + 3z + 2t = 116
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Răspuns :

Danamocanu71
x/2=y/3=z/5=t/7=k
⇒x/2=k⇒x=2k;
⇒y/3=k⇒y=3k;
⇒z/5=k⇒z=5k;
⇒t/7=k⇒t=7k;
⇒7x+5y+3z+2t=116
⇒7·2k+5·3k+3·5k+2·7k=116
⇒14k+15k+15k+14k=116
⇒58k=116
⇒k=2;
⇒x=2·2⇒x=4;
⇒y=3·2⇒y=6;
⇒z=5·2⇒z=10;
⇒t=7·2⇒t=14;
Cristinaioana2
(x;y;z;t) d.p.(2;3;5;7)
7x+5y+3z+2t=116
[tex] \frac{x}{2} = \frac{y}{3} = \frac{z}{5} = \frac{t}{7} [/tex]⇒
x=2K
y=3K
z=5K
t=7K
7×2K+5×3K+3×5K+2×7K=116
14K+15K+15K+14K=116
58K=116
K=116:58
K=2
x=2×2=4
y=2×3=6
z=2×5=10
t=2×7=14
Verificare:7×4+5×6+3×10+2×14=28+30+30+28=116

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