Question: A science journalist reports that a lab uses two reagents, A and B, costing $ \$12 $ and $ \$8 $ per unit, respectively. If 15 units total cost $ \$156 $, how many units of reagent A were purchased?

["How Many Units of Reagent A Were Used? A Clear Breakdown Using Algebra", "When tackling real-world budgeting problems in science labs, careful analysis turns a simple cost question into a powerful logic challenge. A recent report from a science journalist breaks down the purchasing of two key reagents—A and B—offering an opportunity to apply algebra for precise answers. The scenario: a lab buys reagents A and B, priced at $12 and $8 per unit, with a total of 15 units costing $156. The key question: how many units of reagent A were purchased?", "### Setting Up the Equations", "Let:\n- $ x $ = number of units of reagent A\n- $ y $ = number of units of reagent B", "From the problem, we derive two equations based on the given information.", "1. Total units equation: \n$ x + y = 15 $ \nThis reflects the total quantity purchased.", "2. Total cost equation: \n$ 12x + 8y = 156 $ \nThis accounts for the combined cost at $12 per unit for A and $8 per unit for B.", "### Solving the System of Equations", "Start with the first equation:\n$ y = 15 - x $", "Substitute this expression for $ y $ into the cost equation:\n$ 12x + 8(15 - x) = 156 $", "Expand and simplify:\n$ 12x + 120 - 8x = 156 $\n$ 4x + 120 = 156 $\n$ 4x = 36 $\n$ x = 9 $", "### Conclusion", "The lab purchased 9 units of reagent A and $ 15 - 9 = 6 $ units of reagent B. Verifying:\n$ 9 \ imes 12 = 108 $ and $ 6 \ imes 8 = 48 $, totaling $ 156 — matching the report exactly.", "This straightforward yet insightful problem demonstrates how rational reasoning and algebra help clarify complex lab budgets. For journalists and scientists alike, understanding such calculations ensures transparency and accurate reporting on resource allocation in scientific research."]