A contestant on a quiz show gets 50 points for every correct answer and loses 100 points for each incorrect answer. After answering 24 questions, the contestant has 300 points. How many questions has the contestant answered correctly? Incorrectly?

300=50R-100W

R+W=24 or R=24-W

300=50(24-W)-100W
= 1200-50W-100W
150W=900
W=...

so the wrong answers are 6 and the right answers are 18?

To solve this problem, we can set up a system of equations. Let's denote the number of correct answers as "C" and the number of incorrect answers as "I".

Since the contestant gets 50 points for every correct answer and loses 100 points for each incorrect answer, we can write the equation for the total score as:
50C - 100I = 300 (equation 1)

Since the contestant has answered a total of 24 questions, we can write the equation for the total number of questions as:
C + I = 24 (equation 2)

Now, we have two equations with two unknowns (C and I), so we can solve this system of equations to find their values.

One way to solve this system is by substitution. Let's solve equation 2 for C and substitute it into equation 1:
C = 24 - I

Substituting this value into equation 1:
50(24 - I) - 100I = 300

Expanding the equation:
1200 - 50I - 100I = 300

Combining like terms:
-150I = -900

Dividing both sides by -150:
I = 6

Now that we have the value for I, we can substitute it back into equation 2 to find the value for C:
C + 6 = 24

Subtracting 6 from both sides:
C = 18

Therefore, the contestant has answered 18 questions correctly and 6 questions incorrectly.