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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?

JayTRGA  Oct 27, 2015

Best Answer 

 #2
avatar+78741 
+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

 

 

cool cool cool

CPhill  Oct 27, 2015
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3+0 Answers

 #1
avatar+91045 
+10

3T+11M=100

 

M123456789
pts for Multiple choice112233445566778899
Points left89786756453423121
Is left over divisable  by 3NYNNYNNYN
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

 

laughlaughlaugh

 

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
edited by Melody  Oct 27, 2015
edited by Melody  Oct 27, 2015
 #2
avatar+78741 
+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

 

 

cool cool cool

CPhill  Oct 27, 2015
 #3
avatar+91045 
0

Thanks Chris,

I did not see the bit about there being exactly 20 questions.    blush

Melody  Oct 27, 2015

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