Tina's team entered a math contest where teams of students compete by answering questions that are worth either 3 or 5 points. No partial credit is given. Tina's team scored 44 points on 12 questions. How many 5-point questions did the team answer correctly?

Question

anonymous · Answer

7(5)+3(3)=44

whpalmer4 · Answer

@Luis_Rivera 

let f be the number of 5 point questions, and t be the number of 3 point questions
$f + t = 12$ (12 questions altogether)
$5f + 3t = 44$  (44 points scored)

$$f = 12 - t$$$$5(12-t) + 3t = 44$$$$60 -5t + 3t = 44$$$$-2t + 16 = 0$$$$t = 8$$$$f = 12 - 8 = 4$$
So they answered 8 3 point questions and 4 5 point questions.

whpalmer4 · Answer

Always check your work against the problem.  Luis' solution is incorrect because it doesn't involve 12 questions, it involves 7+3 = 10 questions.  8+4 = 12, 8*3 + 4*5 = 24 + 20 = 44.