Răspuns:
24 scanduri de brad
16 scanduri de stejar
Explicație pas cu pas:
O scandura de brad cantareste 5 intregi 1/2 kg, iar una de stejar cantareste 7 intregi 1/4 kg. Intr-o remorca s-au incarcat 40 de scanduri, care cantaresc in total 248 kg. Cate scanduri de brad sunt? Dar de stejar?
Notam cu
b - numarul scandurilor de brad
s - numarul scandurilor de stejar
b + s = 40
Cat cantareste o scandura de brad?
[tex]5\frac{1}{2} = \frac{5*2+1}{2} = \frac{11}{2} = 5,5 \: kg[/tex]
Cat cantareste o scandura de stejar?
[tex]7\frac{1}{4}=\frac{7*4+1}{4 } = \frac{28+1}{4} = \frac{29}{4} = 7,25 \: kg[/tex]
5,5 * b +7,25 * s = 248
[tex]b + s = 40 \Rightarrow b = 40-s\\\\5,5*b+7,25*s = 248\\\\5,5 * (40-s) +7,25s = 248\\\\220 -5,5 s +7,25s = 248\\\\220+ 1,75s = 248\\\\1,75s = 248-220\\\\1,75s = 28\\\\ s = 28 : 1,75 \Rightarrow \boxed{s =16}\\\\ b +16 = 40 \Rightarrow b = 40-16 \Rightarrow \boxed{b=24}[/tex]
