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Giải bài 4 trang 24 Chuyên đề học tập Toán 10 – Chân trời sáng tạo

Một viên lam ngọc và hai viên hoàng ngọc trị giá gấp 3 lần một viên ngọc bích

ꦬTổng hợp đề thi học kì 2 lớp 10 tất cả các môn - Chân trời sáng tạo

Toán - Văn - Anh - Lí - Hóa - Sinh - Sử - Địa...
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Đề bài

Một viên lam ngọc và hai viên hoàng ngọc trị giá gấp 3 lần một viên ngọc bích. Còn bảy viên lam ngọc và một viên hoàng ngọc trị giá gấp 8 lần một viên ngọc bích. Biết giá tiền của bộ ba viên ngọc này là 270 triệu đồng. Tính giá tiền mỗi viên ngọc.

Lời giải chi tiết

Gọi giá tiền mỗi viên lam ngọc, hoàng ngọc, ngọc bích là x,y, z (đơn vị triệu đồng).Một viên lam ngọc và hai viên hoàng ngọc trị giá gấp 3 lần một viên ngọc bích hay \(x + 2y = 3z\)Bảy viên lam ngọc và một viên hoàng ngọc trị giá gấp 8 lần một viên ngọc bích hay \(7x + y = 8z\)Giá tiền của bộ ba viên ngọc này là 270 triệu đồng hay \(x + y + z = 270\)Từ đó ta có hệ phương trình\(\left\{ \begin{array}{l}x + 2y = 3z\\7x + y = 8z\\x + y + z = 270\end{array} \right.\)Dùng máy tính cầm tay giải HPT, ta được \(x = 90,y = 90,z = 90\)Vậy mỗi viên ngọc trị giá 90 triệu đồng.

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