Solution: The ratio of emissions is $4:7:9$. Let the common multiplier be $x$. Then the second borough emitted $7x = 147$ metric tons. Solving for $x$:
["Understanding Emissions Distribution: A Step-by-Step Solution to the Ratio $4:7:9$", "When analyzing environmental data, emission ratios provide critical insights into pollution sources across different boroughs. One such scenario involves a ratio of emissions across three boroughs expressed as $4:7:9$. This ratio simplifies the comparison of their contributions to total emissions, enabling clearer policy decisions and resource allocation.", "### The Emissions Ratio and Common Multiplier", "In emissions analysis, ratios like $4:7:9$ represent proportional contributions. Let the common multiplier be $x$, so actual emissions are expressed as:\n- Borough 1: $4x$ metric tons\n- Borough 2: $7x$ metric tons\n- Borough 3: $9x$ metric tons", "According to the problem, the second borough emitted exactly 147 metric tons. Substituting into the expression:\n$$\n7x = 147\n$$", "### Solving for $x$", "To find the value of $x$, divide both sides by 7:\n$$\nx = \frac{147}{7} = 21\n$$", "### Emissions Outputs", "Now, substituting $x = 21$ back into the expressions:\n- Borough 1: $4x = 4 \ imes 21 = 84$ metric tons\n- Borough 2: $7x = 147$ metric tons (given)\n- Borough 3: $9x = 9 \ imes 21 = 189$ metric tons", "Verification: Total emissions = $84 + 147 + 189 = 420$ metric tons\nRatio check: $84:147:189$ simplifies by dividing each term by 21 → $4:7:9$, confirming accuracy.", "### Conclusion", "Using the ratio $4:7:9$ and a common multiplier $x$, we found $x = 21$. This reveals Borough 2’s emissions at 147 metric tons—a key figure for environmental monitoring and targeted climate action. Clear modeling with ratios strengthens data-driven decision-making in urban sustainability planning."]
