Question

37. impartiti numarul 68 in parti direct proportionale cu 4, 5 ,8
38. impartiti numarul 77 in parti invers proportionale cu 2, 4,si 6

Answer 1

a+b+c=68
$\frac{a}{4}= \frac{b}{5}= \frac{c}{8} = \frac{a+b+c}{4+5+8}= \frac{68}{17} =4$
$\frac{a}{4}=4 => a=16 \\ \frac{b}{5}=4 => b=20 \\ \frac{c}{8}=4 =>c=32$
Solutie: 16,20,32
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77=a+b+c
$\frac{a}{ \frac{1}{2} } = \frac{b}{ \frac{1}{4} } = \frac{c}{ \frac{1}{6} }= \frac{a+b+c}{ \frac{1}{2}+ \frac{1}{4}+ \frac{1}{6} } = \frac{77}{ \frac{6+3+2}{12} }= \frac{77}{ \frac{11}{12} }=77* \frac{12}{11} =84$
$\frac{a}{ \frac{1}{2} }=84 => a=84* \frac{1}{2} =42$
$\frac{b}{ \frac{1}{4} }=84 => b=84* \frac{1}{4}=21$
$\frac{c}{ \frac{1}{6} } =84 => c=84* \frac{1}{6}=14$
Solutie: 42,21,14