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Giải bài 7 trang 8 SBT toán 7 - Chân trời sáng tạo

Tìm ba số a, b, c biết rằng \(a:b:c = 3:2:2\) và \(a + b - c = 99\).

♌Tổng hợp đề thi học kì 2 lớp 7 tất cả các môn - Chân trời sáng tạo

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Đề bài

Tìm ba số a, b, c biết rằng \(a:b:c = 3:2:2\) và \(a + b - c = 99\).

Phương pháp giải - Xem chi tiết

Bước 1: Áp dụng định nghĩa dãy tỉ số bằng nhau Nếu \(a:b:c = d:e:f\) thì \(\frac{a}{d} = \frac{b}{e} = \frac{c}{f}\) Bước 2: Áp dụng tính chất 2 của dãy tỉ số bằng nhau: \(\frac{a}{b} = \frac{c}{d} = \frac{e}{f} = \frac{{a + c + e}}{{b + d + f}} = \frac{{a - c + e}}{{b - d + f}}\) (với \(b + d + f \ne 0,\,b - d + f \ne 0\)).

Lời giải chi tiết

Từ \(a:b:c = 3:2:2\) ta có \(\frac{a}{3} = \frac{b}{2} = \frac{c}{2}\)Áp dụng tính chất của dãy tỉ số bằng nhau ta có:\(\frac{a}{3} = \frac{b}{2} = \frac{c}{2} = \frac{{a + b - c}}{{3 + 2 - 2}} = \frac{{99}}{3} = 33\)Suy ra \(\frac{a}{3} = 33 \Rightarrow a = 99\); \(\frac{b}{2} = 33 \Rightarrow b = 66\); \(\frac{c}{2} = 33 \Rightarrow c = 66\)Vậy \(a = 99;\,b = 66;\,c = 66\).

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