A test has twenty questions worth 100 points the test consists of true or false worth 3 points each and multiple choice ouestions worth 11 p

Question

A test has twenty questions worth 100 points the test consists of true or false worth 3 points each and multiple choice ouestions worth 11 points each how many multiple choice questions are there in test

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Luna 4 days 2021-10-10T21:30:50+00:00 2 Answers 0 views 0

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    0
    2021-10-10T21:32:15+00:00

    Answer:

    5 multiple choice questions and 15 true or false questions

    0
    2021-10-10T21:32:33+00:00

    Let ‘ a ‘ be the number of True/False questions and ‘ b ‘ be the the number MCQ questions.

    Total questions = 30.

    It means,

    a + b = 20 _____________ ( ! )

    It is also given that the true/false questions are worth 3 points. So  the number of points we could score on these questions :

    • 3 × a  

    The Multiple Choice questions are worth 11 points each. So  the number of points we could score on these questions :

    • 11 × b

    Now,

    if we add up the total number of points possible, the result will be

    100 points.

    That is,

    3a + 11b = 100 ________ ( !! )

    Now,

    Observe ( ! )  and subtract a  from both sides. After the subtraction
    ,

    b  will be canceled from the left side and the equation formed will be :

    a = 20 – b

    Now,

    substitute the value of ‘ a ‘ in question ( !! ).

    We get,

    3(20 – b) + 11b = 100

    ⇒ 60 – 3b + 11 b = 100

    ⇒ 60 + 8b = 100

    ⇒  8b = 100 – 60

    ⇒ 8b = 40

    ⇒ b = 40/8

    ∴ b = 5

    Hence,

    There were total 5 MCQ questions in the test.

    \rule{200}2

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