Решебник по математике 6 класс Мерзляк ФГОС Задание 1394

 

\[\boxed{\mathbf{1394}\mathbf{.}\mathbf{\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\ Разделим\ число\ 96\ на\ три\]

\[\ части:\ x,\ y,\ z;\]

\[Выразим\ x:\]

\[\frac{x}{y} = \frac{3}{4}\]

\[4x = 3y\]

\[x = \frac{3}{4}\text{y.\ }\]

\[Выразим\ y:\]

\[\frac{y}{z} = \frac{4}{9}\]

\[4z = 9y\]

\[z = \frac{9}{4}\text{y.}\]

\[Получим:\]

\[\frac{3}{4}y + y + \frac{9}{4}y = 96\]

\[\frac{12}{4}y + y = 96\]

\[3y + y = 96\]

\[4y = 96\]

\[y = 24.\ \]

\[x = \frac{3}{4}y = \frac{3}{4} \cdot 24 = 3 \cdot 6 = 18.\]

\[z = \frac{9}{4}y = \frac{9}{4} \cdot 24 = 9 \cdot 6 = 54.\]

\[Ответ:18;\ 24;\ 54.\]

\[2)\ Разделим\ число\ 185\ на\]

\[\ три\ части\ x,\ y,\ z;\]

\[Выразим\ x:\]

\[\frac{x}{y} = \frac{3}{2}\]

\[2x = 3y\]

\[x = \frac{3}{2}\text{y.}\]

\[Выразим\ z:\]

\[\frac{y}{z} = \frac{2\frac{1}{2}}{3}\]

\[\frac{5}{2}z = 3y\]

\[z = 3y \cdot \frac{2}{5}\]

\[z = \frac{6}{5}\text{y.}\]

\[Получим:\]

\[\frac{3}{2}y + y + \frac{6}{5}y = 185\]

\[\frac{15}{10}y + \frac{12}{10}y + y = 185\]

\[\frac{27}{10}y + y = 185\]

\[\frac{37}{10}y = 185\]

\[y = 185\ :\frac{37}{10} = 185 \cdot \frac{10}{37}\]

\[y = 5 \cdot 10 = 50.\]

\[x = \frac{3}{2}y = \frac{3}{2} \cdot 50 = 3 \cdot 25 = 75.\]

\[z = \frac{6}{5}y = \frac{6}{5} \cdot 50 = 6 \cdot 10 = 60.\ \]

\[Ответ:75;\ 50;\ 60.\ \]