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algebra intermediate

Problem

Suppose

\frac{a}{b} = \frac{3}{5}

,

\frac{b}{c} = \frac{15}{6}

, and

\frac{c}{d} = 6

. What is the value of

\frac{a}{d}

? Express your answer in simplest form.

Solution

Multiply all three equations to find that

\frac{a}{b} \cdot \frac{b}{c} \cdot \frac{c}{d} \frac{a}{d} = \frac{3}{5} \cdot \frac{15}{6} \cdot \frac{6}{1} ⟹ = 9 .

Final answer

9