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Giải bài 6.28 trang 17 sách bài tập toán 9 - Kết nối tri thức tập 2

Một phòng họp lúc đầu có một số dãy ghế với tổng cộng 40 chỗ ngồi. Do phải sắp xếp 55 chỗ ngồi cho một cuộc họp nên người ta kê thêm một dãy ghế và mỗi dãy ghế sắp xếp thêm một chỗ ngồi. Hỏi lúc đầu có mấy dãy ghế trong phòng họp đó?

Tổng hợp Đề thi vào 10 có đáp án và lời giải

Toán - Văn - Anh
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Đề bài

Một phòng họp lúc đầu có một số dãy ghế với tổng cộng 40 chỗ ngồi. Do phải sắp xếp 55 chỗ ngồi cho một cuộc họp nên người ta kê thêm một dãy ghế và mỗi dãy ghế sắp xếp thêm một chỗ ngồi. Hỏi lúc đầu có mấy dãy ghế trong phòng họp đó?

Phương pháp giải - Xem chi tiết

Các bước giải một bài toán bằng cách lập phương trình:

Bước 1. Lập phương trình:

- Chọn ẩn số và đặt điều kiện thích hợp 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 3ꦏ. Trả lời: Kiểm tra xem trong các nghiệm của phương trình, nghiệm nào thỏa mãn điều kiện của ẩn, nghiệm nào không, rồi kết luận.

Lời giải chi tiết

Gọi số dãy ghế trong phòng họp lúc đầu là x (dãy). Điều kiện \(x > 0\), x là ước của 40. Số chỗ ngồi ở mỗi dãy ghế ban đầu là \(\frac{{40}}{x}\) (chỗ ngồi). Số chỗ ngồi ở mỗi dãy ghế sau khi kê thêm một dãy ghế cho 55 người ngồi là \(\frac{{55}}{{x + 1}}\) (chỗ ngồi). Do phải sắp xếp 55 chỗ ngồi cho một cuộc họp nên người ta kê thêm một dãy ghế và mỗi dãy ghế sắp xếp thêm một chỗ ngồi nên ta có phương trình \(\frac{{55}}{{x + 1}} - \frac{{40}}{x} = 1\) Nhân cả hai vế của phương trình này với \(x\left( {x + 1} \right)\) để khử mẫu ta được: \(55x - 40\left( {x + 1} \right) = x\left( {x + 1} \right)\) \({x^2} - 14x + 40 = 0\) Vì \(\Delta ' = {\left( { - 7} \right)^2} - 1.40 = 9\) nên phương trình có hai nghiệm \({x_1} = \frac{{7 + \sqrt 9 }}{1} = 10\) (thỏa mãn) và \({x_2} = \frac{{7 - \sqrt 9 }}{1} = 4\) (thỏa mãn). Vậy trong phòng họp ban đầu có 4 dãy ghế, mỗi dãy có 10 chỗ ngồi hoặc có 10 dãy ghế, mỗi dãy có 4 chỗ ngồi

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Tham Gia Group Dành Cho Lớp 9 - Ôn Thi Vào Lớp 10 Miễn Phí

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