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Giải bài 5.42 trang 35 SGK Toán 8 - Cùng khám phá

Một hỗn hợp kim loại nặng 17,6 g gồm sắt (Fe) và đồng (Cu),
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Đề bài

Một hỗn hợp kim loại nặng 17,6 g gồm sắt (Fe) và đồng (Cu), trong đó khối lượng sắt gấp 1,75 lần khối lượng đồng. Tính thành phần phần trăm khối lượng mỗi kim loại trong hỗn hợp.

Phương pháp giải - Xem chi tiết

Vận dụng phương trình bậc nhất một ẩn để giải quyết nhiều vấn đề thực tiễn theo các bước sau: Bước 1: Lập phương trình -         Chọn ẩn số và đặt điều kiện cho ẩn số -         Biểu diễn các đại lượng chưa biết theo ẩn và các đại lượng đã biết -         Lập phương trình biểu thị mối quan hệ giữa các đại lượng Bước 2: Giải phương trình Bước 3: Kiểm tra xem nghiệm có thỏa mãn điều kiện của ẩn hay không rồi kết luận.

Lời giải chi tiết

Gọi khối lượng kim loại đồng là \(x\) (g)Thì khối lượng kim loại sắt là \(17,6 - x\) (g)Trong đó khối lượng sắt gấp 1,75 lần khối lượng đồng.Ta có phương trình:\(\begin{array}{l}17,6 - x = 1,75x\\17,6 = 1,75x + x\\x = 6,4\left( {tm} \right)\end{array}\)Vậy khối lượng kim loại đồng là 6,4 g, phần trăm kim loại đồng trong hỗn hợp là: \(\frac{{6,4}}{{17,6}}.100 = 36\% \).Khối lượng kim loại sắt là 11,2, phần trăm kim loại sắt trong hỗn hợp là: \(\frac{{11,2}}{{17,6}}.100 = 64\% \).

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