+12 A test has twenty questions worth 100 points. The test consists of True/False questions worth 3 points each and multiple choice questions worth 11 points each. How many multiple choice questions are on the test?
+128408 Let C be the number of T/F questions and M be the number of multiple choice questions....and we have this system of equations :
C + M = 20 → 3C + 3M = 60 → - 3C - 3M = -60 (1)
3C + 11M = 100 (2)
Add (1) and (2) together
8M = 40 divide both sides by 8
M = 5 this is the number of multiple choice questions
C + 5 = 20 → C = 15 this is the number of T/F questions
+118608 3T+11M=100
| M | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| pts for Multiple choice | 11 | 22 | 33 | 44 | 55 | 66 | 77 | 88 | 99 |
| Points left | 89 | 78 | 67 | 56 | 45 | 34 | 23 | 12 | 1 |
| Is left over divisable by 3 | N | Y | N | N | Y | N | N | Y | N |
| How many T/F | 26 | 15 | 4 |
So if could be
2 Multiple choice and 26 T/F check 2*11+26*3 = 100
5 Multiple choice and 15 T/F check 5*11+15*3 = 100
8 Multiple choice and 4 T/F check 8*11+4*3 = 100
Incidentally this is a diophantine equation because all solutions must be integers.
There is a more formal way of solving so that all solutions are found. (including negative solutions)
Of course you problems does not have any negative solutions :))
+128408 Let C be the number of T/F questions and M be the number of multiple choice questions....and we have this system of equations :
C + M = 20 → 3C + 3M = 60 → - 3C - 3M = -60 (1)
3C + 11M = 100 (2)
Add (1) and (2) together
8M = 40 divide both sides by 8
M = 5 this is the number of multiple choice questions
C + 5 = 20 → C = 15 this is the number of T/F questions
