Question

Tìm 3 số a,b,c biết 3a=2b;5b=7c và 3a+5b-7c=60

 

Answer 1

Ta có : 

\(3a=2b\Rightarrow\frac{a}{2}=\frac{b}{3}\Rightarrow\frac{a}{14}=\frac{b}{21}\left(1\right)\)

\(5b=7c\Rightarrow\frac{b}{7}=\frac{c}{5}\Rightarrow\frac{b}{21}=\frac{c}{15}\left(2\right)\)

Từ \(\left(1\right);\left(2\right)\)

\(\Rightarrow\frac{a}{14}=\frac{b}{21}=\frac{c}{15}\)

\(\Rightarrow\frac{3a}{42}=\frac{5b}{105}=\frac{7c}{105}\)

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

\(\frac{3a}{42}=\frac{5b}{105}=\frac{7c}{105}=\frac{3a+5b-7c}{42+105-105}=\frac{60}{42}=\frac{10}{7}\)

\(\Rightarrow\hept{\begin{cases}\frac{3a}{42}=\frac{10}{7}\\\frac{5b}{105}=\frac{10}{7}\\\frac{7c}{105}=\frac{10}{7}\end{cases}\Rightarrow\hept{\begin{cases}\frac{a}{14}=\frac{10}{7}\\\frac{b}{21}=\frac{10}{7}\\\frac{c}{15}=\frac{10}{7}\end{cases}\Rightarrow}\hept{\begin{cases}a=\frac{10}{7}.14=20\\b=\frac{10}{7}.21=30\\c=\frac{10}{7}.15=\frac{150}{7}\end{cases}}}\)

Vậy \(a=20;b=30;c=\frac{150}{7}\)

~ Ủng hộ nhé 

Answer 2

\(3a=2b\Rightarrow\frac{a}{2}=\frac{b}{3}\Rightarrow\frac{a}{14}=\frac{b}{21}\)

\(5b=7c\Rightarrow\frac{b}{7}=\frac{c}{5}\Rightarrow\frac{b}{21}=\frac{c}{15}\)

\(\Rightarrow\frac{a}{14}=\frac{b}{21}=\frac{c}{15}\)

\(\Rightarrow\frac{3a}{42}=\frac{5b}{105}=\frac{7c}{105}=\frac{3a+5b-7c}{42+105-105}\)

\(=\frac{60}{42}=\frac{10}{7}\)

\(\Leftrightarrow\frac{a}{14}=\frac{b}{21}=\frac{c}{15}=\frac{10}{7}\)