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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?

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)

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   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 :))

Oct 27, 2015
edited by Melody  Oct 27, 2015
edited by Melody  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)

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
#3
0

Thanks Chris,

I did not see the bit about there being exactly 20 questions. Oct 27, 2015