Answered

At Westonci.ca, we make it easy to get the answers you need from a community of informed and experienced contributors. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.

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

Sagot :

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]


We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.