Đổi 18 kg = 18000 g

Một gói có số gam muối là :

  18000 : 240 = 75 ( gam )

                   Đáp số : 75 ( gam )

theo bài ra ta có:

\(\frac{a}{b+c+d}=\frac{b}{a+c+d}=\frac{c}{a+b+d}=\frac{d}{a+b+c}\)

=> \(\frac{a}{b+c+d}+1=\frac{b}{a+c+d}+1=\frac{c}{a+b+d}+1=\frac{d}{a+b+c}+1\)

=> \(\frac{a+b+c+d}{b+c+d}=\frac{a+b+c+d}{a+c+d}=\frac{a+b+c+d}{a+b+d}=\frac{a+b+c+d}{a+b+c}\)

=> b+c+d = a+c+d => a=b

a+c+d = a+b+d => b = c

a+b+d = a+b+c => c = d

a+b+c = b+c+d => a = d

=> a = b = c = d

=> \(\frac{a+b}{c+d}+\frac{b+c}{a+d}+\frac{c+d}{a+b}+\frac{d+a}{b+c}=1+1+1+1=4\)

vậy \(\frac{a+b}{c+d}+\frac{b+c}{a+d}+\frac{c+d}{a+b}+\frac{d+a}{b+c}=4\)

bài 1:

theo bài ra ta có:

\(\frac{a}{b}=\frac{c}{d}\)

=>\(\frac{a}{b}=\frac{c}{d}=\frac{2c}{2d}\)

áp dụng tính chất dãy tỉ số bằng nhau ta có:

\(\frac{a}{b}=\frac{c}{d}=\frac{2c}{2d}=\frac{a+c}{b+d}=\frac{a+2c}{b+2d}\)

=> \(\frac{a+c}{b+d}=\frac{a+2c}{b+2d}\)

=> (a+c).(b+2d) = (b+d).(a+2c) (đpcm)

\(\left(1+\frac{1}{2}\right)\left(1+\frac{1}{3}\right)\left(1+\frac{1}{4}\right)...\left(1+\frac{1}{99}\right)\)

\(=\frac{3}{2}.\frac{4}{3}.\frac{5}{4}...\frac{100}{99}=\frac{3.4.5...100}{2.3.4...99}=\frac{100}{2}=50\)