Question

De Pasti un cioban a vandut carne de miel astfel:luni 1\3 din intreaga cantitate,marti 2\3 din rest,miercuri 3\5 din noul rest,joi4\5 din ce a ramas,iar ultimile 120kg in mod egal in zilele de vineri si sambata. Cate kg de carne a vandut?​

Answer 1

x-cantitatea de carne totală pe care a vândut-o

$\frac{1}{3} \times x = \frac{x}{3} \: (luni)$

$x - \frac{x}{3} = \frac{3x}{3} - \frac{x}{3} = \frac{2x}{3} \: (primul \: rest)$

$\frac{2}{3} \times \frac{2x}{3} = \frac{4x}{9} \: (marti)$

$\frac{2x}{3} - \frac{4x}{9} = \frac{6x}{9} - \frac{4x}{9} = \frac{2x}{9} \: (al \: doilea \: rest)$

$\frac{3}{5} \times \frac{2x}{9} = \frac{6x}{45} = \frac{2x}{15} \: (miercuri)$

$\frac{2x}{9} - \frac{2x}{15} = \frac{10x}{45} - \frac{6x}{45} = \frac{4x}{45} \: (al \: treilea \: rest)$

$\frac{4}{5} \times \frac{4x}{45} = \frac{16x}{225} \: (joi)$

$\frac{x}{3} + \frac{4x}{9} + \frac{2x}{15} + \frac{16x}{225} + 120 = x \: | \times 225$

$75x + 100x + 30x + 16x + 27000 = 225x$

$175x + 30x + 16x - 225x = - 27000$

$221x - 225x = - 27000$

$- 4x = - 27000 \: | \div ( - 4)$

$x = 6750 \: kg$