Ratios within Ratios

If the ratio $a:b$ is $2:5$ and the ratio $b:c$ is $3:10$. What is the ratio $a:c$?

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Solution

The $b$ part of each ratio has a LCM of $\mathrm{15}$. Multiplying each ratio so that the $b$ part is 15, we get $6:15$ for the ratio $a:b$ and $15:50$ for the ratio $b:c$. So, the ratio $a:c$ is $6:50$, which simplifies to $3:25$

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