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Giải bài 5.33 trang 30 SGK Toán 8 - Cùng khám phá

Một đội thợ mỏ theo kế hoạch cần khai thác 30 tấn than mỗi ngày. Nhờ cải tiến kĩ thuật, đội đã khai thác được 42 tấn mỗi ngày.
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Đề bài

Một đội thợ mỏ theo kế hoạch cần khai thác 30 tấn than mỗi ngày. Nhờ cải tiến kĩ thuật, đội đã khai thác được 42 tấn mỗi ngày. Do đó đội không những hoàn thành kế hoạch trước 12 tiếng mà còn làm vượt chỉ tiêu thêm 3 tấn nữa. Hỏi theo kế hoạch đội thợ mỏ này cần khai thác bao nhiêu tấn than?

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 thời gian dự kiến của đội khai thác than là x (ngày) \(\left( {x > 0} \right)\)Tổng số tấn than đội dự định khai thác được là \(30x\) (tấn)Thực tế thời gian làm là \(x - \frac{{12}}{{24}} = x - \frac{1}{2}\) (ngày)Thực tế đã khai thác được \(42.\left( {x - \frac{1}{2}} \right) = 42x - 21\) (tấn)Vượt chỉ tiêu 3 tấn nên ta có:\(\begin{array}{l}42x - 21 - 20x = 3\\12x = 21 + 3\\12x = 24\\x = 2\\ =  > 30x = 60\end{array}\)Vậy theo kế hoạch đội cần khai thác 60 tấn than.

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