Question

Determinati numerele a, b, c din sirul de rapoarte egale a+2 supra 2=b+3 supra 3=c+4 supra 4=d+5 supra 5 stiind ca 3a+b+d=40

Answer 1

Răspuns:

Explicație pas cu pas:

$\dfrac{a+2}{2} =\dfrac{b+3}{3}=\dfrac{c+4}{4}=\dfrac{d+5}{5},~~si~~3a+b+d=40.\\Amplificam~prima~fractie~cu~3,~=>~\\\dfrac{3a+6}{6} =\dfrac{b+3}{3}=\dfrac{d+5}{5}=\dfrac{3a+6+b+3+d+5}{6+3+5}=\dfrac{40+14}{14}=\dfrac{54}{14}=\dfrac{27}{7}.\\=>~\dfrac{a+2}{2} =\dfrac{27}{7}~=> ~7(a+2)=2*27~=>~7a+14=54~=>~7a=40~=>~a=\dfrac{40}{7} \\=>~\dfrac{b+3}{3} =\dfrac{27}{7}~=> ~7(b+3)=3*27~=>~7b+21=81~=>~7b=60~=>~b=\dfrac{60}{7}$

$=>~\dfrac{c+4}{4} =\dfrac{27}{7}~=> ~7(c+4)=4*27~=>~7c+28=108~=>~7c=80~=>~c=\dfrac{80}{7}\\ =>~\dfrac{d+5}{5} =\dfrac{27}{7}~=> ~7(d+5)=5*27~=>~7d+35=135~=>~7d=100~=>~d=\dfrac{100}{7}$