A. 10 mc, 10 t& f

B. 7 mc, 13 t& f

C. 2 mc, 18 t& f

D. 5 mc, 15 t& f

Answer is D) 5 mc, 15 t& f

you have two unknown variables, thus you need two equations

definitions:

a = quantity of multiple choice questions

b = quantity of true and false questions

100 points = a*11 points/question + b*3 points/question

20 questions = a +b

using 2nd equation, find equation for ’a’:

a = 20 - b

substitute this equation for ’a’ into 1st equation:

100 = 11a + 3b

100 = 11(20 - b) + 3b

100 = 220 - 11b + 3b

100 - 220 = -8b

-120 = -8b

-120/-8 = b

15 = b

resolve 2nd equation now knowing value of ’b’:

a = 20 - b

a = 20 - 15

a = 5

verify solution is correct by substituting values into first equation

11a + 3b = 100

11(5) + 3(15) = 100

55 + 45 = 100

100 = 100 [OK]

verify solution is correct by substituting values into second equation

a + b = 20

5 + 15 = 20

20 = 20 [OK]