Final answer:
The correct equation that represents three times the smaller number plus twice the larger number is 39 is 3x + 2y = 39, aligning with option (a).
Step-by-step explanation:
The question involves creating two equations based on the given information to find the values of two variables, representing two numbers. According to the problem, the sum of two numbers is sixteen, which can be mathematically represented as x + y = 16. Also, it's given that three times the smaller number plus twice the larger number equals thirty-nine, which can be represented as 3x + 2y = 39, if we assume that x is the smaller number and y is the larger number.
Upon reviewing the choices provided:
a) 3x + 2y = 39
b) 2x + 3y = 39
c) 3x - 2y = 39
d) 2x - 3y = 39
It is clear that the correct representation of the equations based on the information given is option (a).