Question 66

What is the proportion equivalent to $$\frac{X}{Y} : \frac{Y}{Z} : \frac{X}{Z}$$, if $$X : Y : Z = 4 : 7 : 9$$?

Solution

$$\frac{X}{Y} : \frac{Y}{Z} : \frac{X}{Z}$$ = $$\frac{4}{7} : \frac{7}{9} : \frac{4}{9}$$

= $$\frac{4\times9}{7\times9}:\frac{7\times7}{9\times7}:\frac{4\times7}{9\times7}$$

= $$\frac{36}{63}:\frac{49}{63}:\frac{28}{63}$$

= 36 : 49 : 28

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