If 2x = 5y and 7y = 10z, what is the value of zx expressed as a common fraction?

yx=25 and zy=710. Multiplying these, 25710= y x z y= z x=725

jmc

algebra intermediate

Problem

2 x = 5 y

and

7 y = 10 z

, what is the value of

\frac{z}{x}

expressed as a common fraction?

Solution

\frac{y}{x} = \frac{2}{5}

and

\frac{z}{y} = \frac{7}{10}

. Multiplying these,

\frac{2}{5} \cdot \frac{7}{10} = \frac{y}{x} \cdot \frac{z}{y} = \frac{z}{x} = \frac{7}{25}

Final answer

\frac{7}{25}