Question

A test has 20 questions worth 100 points. The test consists of true/false questionsworth 3 points each and multiple choice questions worth 11 points each. How many multiple choice questions are on the test?
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 1

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]