To determine which student wrote the correct equation for the description “Six less than [tex]$2q$[/tex] is equal to 13 times the sum of [tex]$q$[/tex] and 12,” let's analyze both equations.
Description Breakdown
- “Six less than [tex]$2q$[/tex]” translates to [tex]$2q - 6$[/tex].
- “Is equal to” translates to [tex]$=$[/tex].
- “13 times the sum of [tex]$q$[/tex] and 12” translates to [tex]$13(q + 12)$[/tex].
Student 1's Equation:
[tex]\[2(q - 6) = 13q + 12\][/tex]
Here, Student 1 interpreted “Six less than [tex]$2q$[/tex]” as [tex]$2(q - 6)$[/tex] and “13 times the sum of [tex]$q$[/tex] and 12” as [tex]$13q + 12$[/tex]. This does not match the correct interpretation of [tex]$2q - 6 = 13(q + 12)$[/tex], so Student 1's interpretation is incorrect.
Student 2's Equation:
[tex]\[2q - 6 = 13(q + 12)\][/tex]
Here, Student 2 interpreted “Six less than [tex]$2q$[/tex]” as [tex]$2q - 6$[/tex] and “13 times the sum of [tex]$q$[/tex] and 12” as [tex]$13(q + 12)$[/tex]. This matches the correct interpretation exactly, so Student 2's interpretation is correct.
Conclusion:
Student 2 is correct because they accurately represented the description. The equation [tex]\(2q - 6 = 13(q + 12)\)[/tex] correctly matches "Six less than [tex]$2q$[/tex] is equal to 13 times the sum of [tex]$q$[/tex] and 12." Therefore, Student 2's work accurately reflects the problem statement.
