CIMC 2022 Part A - Question 4, CEMC UWaterloo

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This problem is tagged with cimc, cimc22, highschool.

(Canadian Intermediate Mathematics Contest 2022, Part A, Question 4, CEMC - UWaterloo)

If $a$, $b$, $c$, and $d$ satisfy $\frac{a}{b} = \frac{2}{3}$ and $\frac{c}{b} = \frac{1}{5}$ and $\frac{c}{d} = \frac{7}{15}$, what is the value of $\frac{ab}{cd}$?

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