Question

a)Impartiti numarul 54 in parti direct proportionale cu 7 si 11.
b)Impartiti numarul 86 in parti direct proportionale cu 1.25 si2.(3).

Answer 1

a)
a+b=54
a/7=b/11=k
a/7=7k
b/11=11k
11k+7k=54
18k=54
k=54:18
k=3
a=3x7=21
b=3x11=33
b)
a+b=86
a/1,25=b/2,(3)=k
a/1,25=1,25k
b/2,(3)=2,(3)k
1,25k+2,(3)k=86
3,583k=86
k=86:3,58(3)
k=24
a=24x1,25=30
b=24x2,(3)=56

Answer 2

a) a+b=54
[tex] \frac{a}{7} = \frac{b}{11} = \frac{a+b}{7+11} = \frac{54}{18}=3 [/tex]
$\frac{a}{7} =3$⇒a=7*3⇒a=21
$\frac{b}{11} =3$⇒b=11*3⇒b=33
b) a+b=86
$\frac{a}{1,25} = \frac{b}{2,(3)} = \frac{a+b}{1,25+2,(3)}= \frac{86}{ \frac{125}{100} + \frac{21}{9} } = \frac{86}{ \frac{5}{4} + \frac{7}{3} } = \frac{86}{ \frac{43}{12} } =86* \frac{12}{43} =24$
$\frac{a}{ \frac{5}{4} } =24$⇒a=24*5/4=30
$\frac{b}{ \frac{7}{3} } =24$⇒b=24*7/3=56