Two numbers have a sum of 45. One number is 3 more than twice the other. What is the larger of the two numbers?

Let $x$ be the smaller number, so the larger is $2x+3$. Their sum is $x+(2x+3)=45$, so $3x=42$ and $x=14$. The larger number is $2(14)+3=31$, choice J. Check: $14+31=45$. The question asks for the larger number, so stopping at $x=14$ is a trap: choice F ($14$) is the smaller number. Choice G ($21$) and choice H ($28$) fail the conditions: $21$ would pair with $24$, and neither pair has one number equal to 3 more than twice the other.