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Question 1 (Multiple Choice, Worth 5 Points): Writing One-Variable Linear Equations (LC)

Two students wrote the following description as an equation:
Six less than [tex]$2q$[/tex] is equal to 13 times the sum of [tex]$q$[/tex] and 12.

\begin{tabular}{|c|c|}
\hline
Student 1 & Student 2 \\
\hline
[tex]2(q-6)=13(q)+12[/tex] & [tex]2q-6=13(q+12)[/tex] \\
\hline
\end{tabular}

Which student is correct, and why?

A. Student 1 is correct because 2 is multiplied by the quantity of [tex][tex]$q$[/tex][/tex] minus 6.
B. Student 1 is correct because 13 is multiplied by the quantity of [tex]q[/tex] plus 12.
C. Student 2 is correct because 2 is multiplied by the quantity of [tex]$q$[/tex] minus 6.
D. Student 2 is correct because 13 is multiplied by the quantity of [tex]$q$[/tex] plus 12.



Answer :

GinnyAnswer
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.

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