Question

[Hoàng Xuân Ngân]

Suppose that 5a=2b and 7b=3c. Find the ratio of ( c-b) to (b-a)

Answer 1

[Hoàng Phúc]

5a=2b<=>a/b=2/5<=>a/2=b/5<=>a/6=b/15(1)

7b=3c<=>b/c=3/7<=>b/3=c/7<=>b/15=c/35(2)

từ (1);(2)=>a/6=b/15=c/35

Theo t/c dãy tỉ số=nhau:

\(\frac{a}{6}=\frac{b}{15}=\frac{c}{35}=\frac{c-b}{35-15}=\frac{b-a}{15-6}\Leftrightarrow\frac{c-b}{20}=\frac{b-a}{9}\Leftrightarrow\frac{c-b}{b-a}=\frac{20}{9}\)

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