Question

A contestant on a quiz show gets 150 points for every correct answer and loses 250 points for each incorrect answer. After answering 20 questions, the contestant has 200 points. How many question has the contestant answered correctly? ard

Answer 1

Given data:

The points obtained after getting correct answer is c=150.

The points losses after getting incorrect answer is i=250.

The expression for total questions is,

`\begin{gathered} c+i=20 \\ i=20-c \end{gathered}`

The expression for total marks is,

`150c-250i=200`

Substitute (20-c) for i in the above expression.

`\begin{gathered} 150c-250(20-c)=200 \\ 150c-5000+250c=200 \\ 400c=5200 \\ c=13 \end{gathered}`

The numbers of incorrect questions are,

`\begin{gathered} i=20-13 \\ =7 \end{gathered}`

Thus, the numbers of correct questions are 13, and numbers of incorrect questions are 7.