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Giải bài 2.17 trang 28 sách bài tập toán 9 - Kết nối tri thức tập 1

Một công ty chuyển nhà cần di chuyển một cây đàn piano nặng 260kg bằng thang máy. Thang máy có thể chở được tối đa là 710kg. a) Viết và giải bất phương trình để xác định khối lượng thang máy có thể chở thêm được. b) Ngoài chiếc đàn piano, thang máy có thể chở thêm được bao nhiêu người biết mỗi người nặng khoảng 60kg.

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

Toán - Văn - Anh
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Đề bài

Một công ty chuyển nhà cần di chuyển một cây đàn piano nặng 260kg bằng thang máy. Thang máy có thể chở được tối đa là 710kg. a) Viết và giải bất phương trình để xác định khối lượng thang máy có thể chở thêm được. b) Ngoài chiếc đàn piano, thang máy có thể chở thêm được bao nhiêu người biết mỗi người nặng khoảng 60kg.

Phương pháp giải - Xem chi tiết

a) + Gọi x(kg) là khối lượng thang máy có thể chở thêm được. + Tổng khối lượng thang máy chở là: \(260 + x\left( {kg} \right)\). + Vì thang máy có thể chở được tối đa là 710kg nên ta có bất phương trình: \(260 + x \le 710\). + Giải bất phương trình, từ đó rút ra kết luận. b) + Gọi \(y\left( {y \in \mathbb{N}} \right)\) là số người thang máy có thể chở thêm được. + Từ dữ kiện bài toán lập được bất phương trình bậc nhất ẩn y. + Giải bất phương trình thu được, kết hợp với điều kiện \(y \in \mathbb{N}\) và đưa ra kết luận.

Lời giải chi tiết

a) Gọi x(kg) là khối lượng thang máy có thể chở thêm được. Suy ra, tổng khối lượng thang máy chở là: \(260 + x\left( {kg} \right)\). Vì thang máy có thể chở được tối đa là 710kg nên ta có bất phương trình: \(260 + x \le 710\). \(x \le 710 - 260\) \(x \le 450\) Vậy thang máy có thể chở thêm được tối đa 450kg. b) Gọi \(y\left( {y \in \mathbb{N}} \right)\) là số người thang máy có thể chở thêm được. Khi đó, \(60y \le 450\), suy ra \(y \le \frac{{15}}{2}\) Mà \(y \in \mathbb{N}\) nên thang máy có thể chở thêm tối đa 7 người.

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