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 questions. How many 5-point questions did the team answer correctly?

Question

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 questions.  How many 5-point questions did the team answer correctly?

amistre64 · Answer

3x+5y = 44

this might be applicable to number theory

amistre64 · Answer

since the gcd of 3 and 5 is 1

determine the solutions to:  3x+5y = 1

5 = 3(1) + 2
3 = 2(1) + 1

               0
       0      1
0-1(1) = -1
1-1(-1) = 2  ;  x=2


 3(2)+5(-1) = 1 ;  y = -1

times it by 44

3(88)+5(-44) = 44

x = 88 + 5n
y = -44 - 3n

solve n  for x,y >0


88 + 5n > 0 ;   n > -88/5,   -17,-16,-15 ....
-44 - 3n >0 ;    n < -44/3  -14,-15,-16

looks like -14 and -15 might be useful if i remembered it correctly

amistre64 · Answer

i think i erred that

44 = 5(8) + 4
44 = 5(7) + 9   <-- possible 3(3)
44 = 5(6) + 14
44 = 5(5) + 19
44 = 5(4) + 24 <-- possible 3(8)
44 = 5(3) + 29
44 = 5(2) + 34
44 = 5(1) + 39 <-- possible 3(13)
44 = 5(0) + 44