Question

There are \[40\] questions in the test booklet of the Mathematics Olympiad. If Stephen scores \[80\] marks when \[5\] marks is awarded for each correct answer and \[3\] marks is deducted for each incorrect answer then find the number of correct answers attempted by Stephen.

Answer 1

Hint: First write down the given questions. We are asked the number of correct answers attempted by Stephen. Assume a value for the number of correct answers, for one correct answer \[5\] mark is awarded, find the total marks given for correct answers, similarly find for incorrect number of answers and form equations to equate with the given values to find the required answer.

Complete step-by-step answer:
Given, total number of questions \[T = 40\]
Marks scored by Stephen is \[M = 80\]
Marks awarded for each correct answer is \[C = 5\]
Marks deducted for each incorrect answer is \[I = 3\]
We are asked to find the number of correct answers attempted by Stephen.
Let the number of correct answer attempted by Stephen be \[x\]
And let number of incorrect answer attempted by Stephen be \[y\]
Total marks awarded on correct answers will be \[CM = x \times 5 = 5x\]
Total marks deducted on incorrect answers will be \[IM = y \times 3 = 3x\]
Total marks will be,
 \[M = CM - IM \\
   \Rightarrow M = 5x - 3y \]
Putting the value of \[M\] , we get
 \[80 = 5x - 3y\]
 \[ \Rightarrow 5x - 3y = 80\] (i)
Total number of questions can also be written as,
 \[T = x + y\]
Putting the value of \[T\] we have,
 \[40 = x + y \\
   \Rightarrow y = 40 - x \]
Putting this value of \[y\] in equation (i), we get
 \[5x - 3\left( {40 - x} \right) = 80 \\
   \Rightarrow 5x - 120 + 3x = 80 \\
   \Rightarrow 8x = 80 + 120 \]
 \[\Rightarrow 8x = 200 \\
   \Rightarrow x = 25 \]
Therefore, the number of correct answers attempted by Stephen is \[25\] .
So, the correct answer is “ \[25\] ”.

Note: In such types of questions, always write down the given quantities at first. Then assume a value for the required answer and form equations. Using the conditions or values given in the questions try to solve those equations and find the required answer.