How many 9 point and 5 point questions are on the test?

Question

An exam worth 408 points contains 52 questions. Some are worth 9 points, and others are worth 5 points. What is the best method to work and solve this 2 system equation word problem?

Answer 1

 N + F = 52 [number of questions]

9N + 5F = 408 [total number of points]

9N + 5F = 408)

- (5N + 5F = 260)

------------------------ [Elimination; subtract equations]

4N = 148

N = 37 questions

37 + F = 52 [plug N into either equation)

F = 15 questions

Check (very important):

Is 9*37 + 5*15 = 408 ?

333 + 75 =408 ?

408 = 406 ?yes

Answer 2

N + F = 52

9N + 5F = 408

Either substitution or elimination will work effectively and as long as the coefficients are small one is not much easier than the other. I personally would multiply the 1st equation by 5 and eliminate the F.