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A question bank has 10 questions worth 100 marks. It consists of multiple choice questions worth 10 marks each and yes/no questions worth 3 marks each. How many multiple choice questions are on the question bank?

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Last updated date: 13th Jun 2024
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Answer
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Hint: Here by considering two variables for 10 mark questions and 3 mark questions we will find two equations with the help of the given conditions, thereby solving the two equations we can find the required answer.

 Complete step by step answer:
It is given that a question bank has 10 questions worth 100 marks also given that it consists of multiple choice questions consisting of 10 marks each and yes/no questions worth 3 marks each.
Let us assume \[x\]as the number of multiple choice questions
Also let\[y\]be the number of Yes/No questions.
Then as per the given statement form the following equations,
Since the total number of question is 10 we get,
\[x + y = 10\]
Let us rearrange the above equation and mark it as (1)
\[y = 10 - x\]……… (1)
Also from the given total marks is 100. Where each multiple choice questions and yes/no questions worth 10 and 3 marks respectively, we get,
\[10x + 3y = 100\]……. (2)
Let us now substitute the value of y from equation (1) in equation (2), we get,
\[10x + 3\left( {10 - x} \right) = 100\]
Let us simply the above equation to find the value of x,
\[10x - 3x = 100 - 30\]
\[7x = 70\]
\[x = 10\]
Substitute the value of x in equation (1) we get,
\[y = 10 - 10 = 0\]
Therefore, we have found that there are 10 multiple choice questions and 0 yes or no questions.

Note:
Here we have two equations and two variables, therefore we have found the values using the equations. If the number of variables equals the number of equations then we can say that there exists a solution. Also since the equations are linear we will solve the equations easily by substituting one equation into the other.