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Giải bài 17 trang 17 sách bài tập toán 9 - Chân trời sáng tạo tập 1

Một trường tuyển 85 học sinh vào hai lớp năng khiếu bóng rổ và bóng chuyền. Nếu chuyển 25 học sinh từ lớp bóng rổ sang lớp bóng chuyền thì số học sinh của lớp bóng chuyền bằng (frac{{12}}{5}) số học sinh lớp bóng rổ. Hãy tính xem mỗi lớp có bao nhiêu học sinh.

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

Toán - Văn - Anh
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Đề bài

Một trường tuyển 85 học sinh vào hai lớp năng khiếu bóng rổ và bóng chuyền. Nếu chuyển 25 học sinh từ lớp bóng rổ sang lớp bóng chuyền thì số học sinh của lớp bóng chuyền bằng \(\frac{{12}}{5}\) số học sinh lớp bóng rổ. Hãy tính xem mỗi lớp có bao nhiêu học sinh.

Phương pháp giải - Xem chi tiết

Dựa vào: Gọi x,y lần lượt là số học sinh của lớp bóng rổ và lớp bóng chuyền (\(x,y \in \mathbb{N}^*\); x,y < 85).

Dựa vào dữ kiện đề bài để lập phương trình.

Giải hệ phương trình và kết luận.

Lời giải chi tiết

Gọi x,y lần lượt là số học sinh của lớp bóng rổ và lớp bóng chuyền (\(x,y \in \mathbb{N}^*\); x,y < 85). Một trường tuyển 85 học sinh vào hai lớp năng khiếu bóng rổ và bóng chuyền ta có phương trình: x + y = 85. Nếu chuyển 25 học sinh từ lớp bóng rổ sang lớp bóng chuyền thì số học sinh của lớp bóng chuyền bằng \(\frac{{12}}{5}\) số học sinh lớp bóng rổ ta có phương trình: Y + 25 = \(\frac{{12}}{5}\)(x – 25). Ta có hệ phương trình: \(\left\{ {\begin{array}{*{20}{c}}{x + y = 85}\\{y + 25 = \frac{{12}}{5}(x - 25)}\end{array}} \right.\)  hay \(\left\{ {\begin{array}{*{20}{c}}{x + y = 85}\\{ - 12x + 5y =  - 425}\end{array}} \right..\) Giải hệ phương trình ta được x = 50, y = 35 (thoả mãn). Vậy lớp bóng rổ có 50 học sinh, lớp bóng chuyền có 35 học sinh.

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