Cho a/2 = b/3, b/5 = c/ 4. Tìm a, b, c biết a + b + c = -74.

Ta có:

⦁\(\frac{a}{2} = \frac{b}{3}\) suy ra \(\frac{a}{{2.5}} = \frac{b}{{3.5}}\) hay \(\frac{a}{{10}} = \frac{b}{{15}}\) (1)

⦁\(\frac{b}{5} = \frac{c}{4}\) suy ra \(\frac{b}{{5.3}} = \frac{c}{{4.3}}\) hay \(\frac{b}{{15}} = \frac{c}{{12}}\)   (2)

Từ (1), (2) suy ra \(\frac{a}{{10}} = \frac{b}{{15}} = \frac{c}{{12}}\).

Áp dụng tính chất dãy tỉ sổ bằng nhau, ta có:

\(\frac{a}{{10}} = \frac{b}{{15}} = \frac{c}{{12}} = \frac{{a + b + c}}{{10 + 15 + 12}} = \frac{{ - 74}}{{37}} = - 2\).

Suy ra a = (–2) . 10 = –20; b = (–2) . 15 = –30; c = (–2) . 12 = –24.

Do đó a = –20; b = –30; c = –24.