Giải Bài 41 trang 54 sách bài tập toán 7 tập 1 - Cánh diều

Đề bài

Tìm số x trong mỗi tỉ lệ thức sau:

a) \(\dfrac{x}{{26}} = \dfrac{{21}}{{39}}\);                                  b) \(4:5,2 = x:\dfrac{2}{7}\);

c) \(\dfrac{{1,25}}{{0,1x}} = \dfrac{{1,35}}{{0,2}}\);                   d*) \((3x - 2):\dfrac{7}{2} = \dfrac{4}{{21}}:\dfrac{1}{{12}}\).

Lời giải chi tiết

a)

\(\begin{array}{l}\dfrac{x}{{26}} = \dfrac{{21}}{{39}}\\{\rm{  }}39.x = 21.26\\{\rm{  }}39.x = 546\\{\rm{  }}x = 546:39\\{\rm{  }}x = 14\end{array}\)                   

Vậy \(x = 14\).                       

b)

 \(\begin{array}{l}4:5,2 = x:\dfrac{2}{7}\\{\rm{  }}4:\dfrac{{26}}{5} = x:\dfrac{2}{7}\\{\rm{  }}x:\dfrac{2}{7} = 4.\dfrac{5}{{26}}\\{\rm{  }}x:\dfrac{2}{7} = \dfrac{{10}}{{13}}\\{\rm{  }}x = \dfrac{{10}}{{13}}.\dfrac{2}{7}\\{\rm{  }}x = \dfrac{{20}}{{91}}\end{array}\)

Vậy \(x = \dfrac{{20}}{{91}}\).

c)

 \(\begin{array}{l}\dfrac{{1,25}}{{0,1x}} = \dfrac{{1,35}}{{0,2}}\\{\rm{ }}1,25{\rm{ }}.{\rm{ }}0,2 = 1,35{\rm{ }}.{\rm{ }}0,1x\\{\rm{ }}0,25 = 0,135x\\{\rm{ }}x = 0,25:0,135\\{\rm{ }}x = \dfrac{{50}}{{27}}\end{array}\)                                         

Vậy \({\rm{ }}x = \dfrac{{50}}{{27}}\).

d*)

\(\begin{array}{l}(3x - 2):\dfrac{7}{2} = \dfrac{4}{{21}}:\dfrac{1}{{12}}\\{\rm{  }}(3x - 2).\dfrac{2}{7} = \dfrac{4}{{21}}.12\\{\rm{  }}\dfrac{{2.(3x - 2)}}{7} = \dfrac{{16}}{7}\\ \to 2.(3x - 2) = 16\\{\rm{  }}3x - 2 = 16:2 = 8\\{\rm{  }}3x = 8 + 2 = 10\\{\rm{  }}x = 10:3\\{\rm{  }}x = \dfrac{{10}}{3}\end{array}\)

Vậy \(x = \dfrac{{10}}{3}\).