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?

Use models, pictures, diagrams, and/or symbols to represent and solve the task situation and select an effective strategy to solve the task. You may attach other files if needed. (SHOW ALL WORK)

Let's represent the number of correct answers as "x" and the number of incorrect answers as "y".

Given that the contestant gets 50 points for every correct answer and loses 100 points for each incorrect answer, we can create the following equations:

1. The total number of questions answered: x + y = 24
2. The total points earned: 50x - 100y = 300

To solve this system of equations, we can use the method of substitution or elimination. Let's use the method of substitution:

From equation 1, we can solve for y in terms of x:
y = 24 - x

Substitute this value of y into equation 2:
50x - 100(24 - x) = 300
50x - 2400 + 100x = 300
150x - 2400 = 300
150x = 2700
x = 2700 / 150
x = 18

Now substitute the value of x into equation 1 to find y:
18 + y = 24
y = 24 - 18
y = 6

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

To solve this task, we can create two equations based on the information given.

Let's represent the number of correct answers as C and the number of incorrect answers as I.

1. The first equation represents the total points earned:
50C - 100I = 300

2. The second equation represents the total number of questions answered:
C + I = 24

To solve this system of equations, we can use substitution or elimination method.

Let's solve it using the substitution method:
From equation 2, we know C = 24 - I.

Substitute this into equation 1:
50(24 - I) - 100I = 300
1200 - 50I - 100I = 300
-150I = 300 - 1200
-150I = -900
I = (-900)/(-150)
I = 6

Substitute the value of I back into equation 2 to find C:
C + 6 = 24
C = 24 - 6
C = 18

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

If there are x correct answers, then there are 24-x mistakes. So, you need to solve

50x - 100(24-x) = 300