Question

Reparta o numero 3200 em partes inversamente proporcionais aos numero 4, 7 e 12.​

Answer 1

Resposta:

Explicação passo a passo:

$a+b+c=3200$

$(a;b;c)=>I.P=>\:(4;7;12)$

$a\:.\:4=b\:.\:7=c\:.\:12=k$

$a=\frac{k}{4}$

$b=\frac{k}{7}$

$c=\frac{k}{12}$

$a+b+c=3200$

$\frac{k}{4}+\frac{k}{7}+\frac{k}{12} =3200$

$mmc(4;7;12)=84$

$\frac{21k}{84} +\frac{12k}{84} +\frac{7k}{84} =\frac{268.800}{84}$

$\frac{21k+12k+7k}{84} =\frac{268.800}{84}$

$40k=268.800$

$k=268.800/40$

$k=6720$

$a=\frac{k}{4}$

$a=\frac{6720}{4}$

$a=1680$

$b=\frac{k}{7}$

$b=\frac{6720}{7}$

$b=960$

$c=\frac{k}{12}$

$c=\frac{6720}{12}$

$c=560$

$(a;b;c)=>(1680;960;560)$