Cagney can frost a cupcake every $$20$$ seconds and Lacey can frost a cupcake every $$30$$ seconds. Working together, how many cupcakes can they frost in $$5$$ minutes? ($$2012$$ AMC $$10\rm A$$ Problem, Question \#$$11$$) 
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Method1: Cagney can frost one in $$20$$ seconds, and Lacey can frost one in $$30$$ seconds. Working together, they can frost one in $$\dfrac{20\cdot30}{20+30}=\dfrac{600}{50}=12$$ seconds. In $$300$$ seconds ( $$5$$ minutes), they can frost $$\boxed{(\text{D})25}$$ cupcakes.  Method2: In $$300$$ seconds ($$5$$ minutes), Cagney will frost $$\dfrac{300}{20}=15$$ cupcakes, and Lacey will frost $$\dfrac{300}{30}=10$$ ~cupcakes. Therefore, working together they will frost $$15+10=\boxed{(\text{D})25}$$ cupcakes.  Method3: Since Cagney frosts $$3$$ cupcakes a minute, and Lacey frosts $$2$$ cupcakes a minute, they together frost $$3+2=5$$ cupcakes a minute. Therefore, in $$5$$ minutes, they frost $$5\times5=25\Rightarrow\boxed{(\text{D})}$$. 