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?

JayTRGA
Oct 27, 2015

#2**+5 **

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

CPhill
Oct 27, 2015

#1**+10 **

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 :))

Melody
Oct 27, 2015

#2**+5 **

Best Answer

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

CPhill
Oct 27, 2015